A principal component analysis-cerebellar model articulation controller (PCA-CMAC) model is proposed for machine performance degradation assessment.PCA is used to feature selection,which eliminates the redundant inf...A principal component analysis-cerebellar model articulation controller (PCA-CMAC) model is proposed for machine performance degradation assessment.PCA is used to feature selection,which eliminates the redundant information among the features from the sensor signals and reduces the dimension of the input to CMAC.CMAC is used to assess degradation states quantitatively based on its local generalization ability.The implementation of the model is presented and the model is applied in a drilling machine to assess the states of the cutting tool. The results show that the model can assess the wear states quantitatively based on the normal state of the cutting tool.The influence of the quantization parameter g and the generalization parameter r in the CMAC model on the assessment results is analyzed.If g is larger,the generalization ability is better,but the difference of degradation states is not obvious.If r is smaller,the different states are distinct,but memory requirements for storing the weights are larger.The principle for selecting two parameters is that the memory storing the weights should be small while the degradation states should be easily distinguished.展开更多
A lifetime prediction method for high-reliability tantalum (Ta) capacitors was proposed, based on multiple degradation measures and grey model (GM). For analyzing performance degradation data, a two-parameter mode...A lifetime prediction method for high-reliability tantalum (Ta) capacitors was proposed, based on multiple degradation measures and grey model (GM). For analyzing performance degradation data, a two-parameter model based on GM was developed. In order to improve the prediction accuracy of the two-parameter model, parameter selection based on particle swarm optimization (PSO) was used. Then, the new PSO-GM(1, 2, co) optimization model was constructed, which was validated experimentally by conducting an accelerated testing on the Ta capacitors. The experiments were conducted at three different stress levels of 85, 120, and 145℃. The results of two experiments were used in estimating the parameters. And the reliability of the Ta capacitors was estimated at the same stress conditions of the third experiment. The results indicate that the proposed method is valid and accurate.展开更多
This paper deals with positive solutions of a degenerate parabolic system: u t= Δ u m+ v p ln α(h+u), v t= Δ v n+u q ln β(h+v) with homogeneous Dirichlet boundary conditions and positive in...This paper deals with positive solutions of a degenerate parabolic system: u t= Δ u m+ v p ln α(h+u), v t= Δ v n+u q ln β(h+v) with homogeneous Dirichlet boundary conditions and positive initial conditions. This system describes the processes of diffusion of heat and burning in two component continuous media with nonlinear conductivity and volume energy release. We obtain the global existence and blow up results of the solution relying on comparison with carefully constructed upper solutions and lower solutions.展开更多
A modified random walk model for human motion is proposed to investigate characteristics of 60GHz indoor office propagation.Compared with the classic random walk model,the movement tendency in the walking process is t...A modified random walk model for human motion is proposed to investigate characteristics of 60GHz indoor office propagation.Compared with the classic random walk model,the movement tendency in the walking process is taken into account in the modified model.Based on the proposed model,path gains of the propagation environment are simulated under a variety of settings by using a ray tracing method.Simulation results and analysis show that human motion is a major source of disturbance to the indoor office propagation and results in performance degradation in some areas.展开更多
This paper studies the conditions of blow up in finite time of solutions of initial boundary value problem for a class nonlinear doubly degenerate parabolic equation.
This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on th...This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988)[1.2] and Seber & Wild (1989)[3].展开更多
In this paper we study the decay estimate of global solutions to the initial-boundary value problem for double degenerate nonlinear parabolic equation by using a dif-ference inequality.
A design and verification of linear state observers which estimate state information such as angular velocity and load torque for retraction control of the motorized seat belt (MSB) system were described. The motorize...A design and verification of linear state observers which estimate state information such as angular velocity and load torque for retraction control of the motorized seat belt (MSB) system were described. The motorized seat belt system provides functions to protect passengers and improve passenger's convenience. Each MSB function has its own required belt tension which is determined by the function's purpose. To realize the MSB functions, state information, such as seat belt winding velocity and seat belt tension are required. Using a linear state observer, the state information for MSB operations can be estimated without sensors. To design the linear state observer, the motorized seat belt system is analyzed and represented as a state space model which contains load torque as an augmented state. Based on the state space model, a linear state observer was designed and verified by experiments. Also, the retraction control of the MSB algorithm using linear state observer was designed and verified on the test bench. With the designed retraction control algorithm using the linear state observer, it is possible to realize various types of MSB functions.展开更多
This research considers the mathematical relationship between concentration of Chla and seven environmental factors, i.e. Lake water temperature (T), Secci-depth (SD), pH, DO, CODMn, Total Nitrogen (TN), Total Phospho...This research considers the mathematical relationship between concentration of Chla and seven environmental factors, i.e. Lake water temperature (T), Secci-depth (SD), pH, DO, CODMn, Total Nitrogen (TN), Total Phosphorus (TP). Stepwise linear regression of 1997 to 1999 monitoring data at each sampling point of Qiandaohu Lake yielded the multivariate regression models presented in this paper. The concentration of Chla as simulation for the year 2000 by the regression model was similar to the observed value. The suggested mathematical relationship could be used to predict changes in the lakewater environment at any point in time. The results showed that SD, TP and pH were the most significant factors affecting Chla concentration.展开更多
The mathematic model of heating chamber for implementing the prediction of the annealing craft and improving the self adapting with the expansion of the new annealing furnace form, new annealing crafts and new kinds o...The mathematic model of heating chamber for implementing the prediction of the annealing craft and improving the self adapting with the expansion of the new annealing furnace form, new annealing crafts and new kinds of steel coil has been established. The model developed which including the temperature for gas in heating chamber and the heating cover is based on the characteristics of anneal craft and the situations of locale production run. Firstly, the characteristic of the heating cover which limits the temperature was considered. Secondly, the locale production run condition and dispatching condition were considered. Finally, combining with the models and the simulation system, the numerical simulation research of the anneal process for the high performance hydrogen bell-type annealer as well as the spot experiment test were carried out. The results obtained from the developed models, usually finished less than thirty seconds, are in fair agreement with the test values, such as the relative errors of annealing times were within ±5%, and the quality' of the annealed steels were guaranteed.展开更多
Objective It has been reported that D-galactose (D-gal) can model subacute aging, and aluminum (AI) acts as a neurotoxin, but combined effects of them have not been reported. The present work aimed to reveal the e...Objective It has been reported that D-galactose (D-gal) can model subacute aging, and aluminum (AI) acts as a neurotoxin, but combined effects of them have not been reported. The present work aimed to reveal the effect of combined administration of D-gal and A1 in mice and compare the effect of D-gal treatment with that of A1 treatment. Meth- ods A1 was intragastricaHy administered and D-gal was subcutaneously injected into Kunming mice for 10 consecutive weeks. Learning and memory, eholinergic systems, as well as protein levels of amyloid β (Aβ) and hyperphosphorylated tau were determined using Morri water maze test, biochemical assays and immunohistochemical staining, respectively. Results The mice with combined treatment had obvious learning and memory deficits, and showed decreases in brain ace- tylcholine (ACh) level and in activities of choline acetyltransferase (CHAT) and acetyleholinesterase (ACHE). Formation of senile plaque (SP)-like and neurofibrillary tangle (NFT)-like structures was also observed. The behavioral and pathologi- cal changes persisted for at least 6 weeks after withdrawal of D-gal and A1. Conclusion Combined use of D-gal and A1 is an effective way to establish the non-transgenic Alzheimer's disease (AD) animal model, and is useful for studies of AD pathogenesis and therapeutic evaluation.展开更多
Polyglutamine (polyQ) diseases are a family of neurodegenerative disorders including Huntington’s disease, spinobulbar muscular atrophy,dentatorubral-pallidoluysian atrophy and several spinocerebellar ataxias.polyQ...Polyglutamine (polyQ) diseases are a family of neurodegenerative disorders including Huntington’s disease, spinobulbar muscular atrophy,dentatorubral-pallidoluysian atrophy and several spinocerebellar ataxias.polyQ diseases are caused by abnormal expansion of CAG repeats in certain genes.The expanded CAG repeats are then translated into a series of abnormally expanded polyQ tracts.Such polyQ tracts may induce misfolding of the disease-causing proteins.The present review mainly focuses on the common characteristics of the pathogenesis of these polyQ diseases,including conformational transition of proteins and its influence on the function of these proteins,the correlation between decreased ability of proteoly-sis and late-onset polyQ diseases,and the relationship between wide expression of disease-causing proteins and selective neuronal death.展开更多
Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is con...Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is contained in R are fixed design points, β =(β_1,β_2,···,β_p)′ is an unknown parameter vector, g(·) is an unknown bounded real-valuedfunction defined on a compact subset T of the real line R, and ε_k is a linear process given byε_k = ∑ from j=0 to ∞ of ψ_je_(k-j), ψ_0=1, where ∑ from j=0 to ∞ of |ψ_j| < ∞, and e_j,j=0, +-1, +-2,···, ard i.i.d. random variables. In this paper we establish the asymptoticnormality of the least squares estimator of β, a smooth estimator of g(·), and estimators of theautocovariance and autocorrelation functions of the linear process ε_k.展开更多
The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with "slow" decay initial data. By con...The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with "slow" decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the life-span of classical solutions are given in the case that the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.1-1.3 in [2] are still valid for this kind of initial data.展开更多
This paper considers the pointwise estimate of the solutions to Cauchy problem for quasilin-ear hyperbolic systems, which bases on the existence of the solutions by using the fundamental solutions. It gives a sharp po...This paper considers the pointwise estimate of the solutions to Cauchy problem for quasilin-ear hyperbolic systems, which bases on the existence of the solutions by using the fundamental solutions. It gives a sharp pointwise estimates of the solutions on domam under consideration. Specially, the estimate is precise near each characteristic direction.展开更多
In this paper, we study the following degenerate critical elliptic equation with anisotropic coefficients-div(|x N | 2α▽u) = K(x)|x N | α·2 * (s)-s |u| 2 * (s)-2 u in R N ,where x = (x 1 , . . . , x N ) ∈ R N...In this paper, we study the following degenerate critical elliptic equation with anisotropic coefficients-div(|x N | 2α▽u) = K(x)|x N | α·2 * (s)-s |u| 2 * (s)-2 u in R N ,where x = (x 1 , . . . , x N ) ∈ R N , N≥3, α > 1/2, 0≤ s ≤2 and 2 * (s) = 2(N-s)/(N-2). Some basic properties of the degenerate elliptic operator -div(|x N |2α▽u) are investigated and some regularity, symmetry and uniqueness results for entire solutions of this equation are obtained. We also get some variational identities for solutions of this equation. As consequences, we obtain some nonexistence results for this equation.展开更多
The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form: μt-△φ(μ) = 0 ,where φ ε C1(R^1) is a strictly monotone increasing function. Cle...The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form: μt-△φ(μ) = 0 ,where φ ε C1(R^1) is a strictly monotone increasing function. Clearly, the above equation has strong degeneracy, i.e., the set of zero points of φ'(.) is permitted to have zero measure. This is an answer to an open problem in [13, p. 288].展开更多
We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniquen...We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniqueness and nonnegativeness of solutions when the principal operator is monotone and the nonlinearity is nonincreasing. Our operator is of the most general form containing all previous ones and we also weaken assumptions on the operator and the nonlinearity to get the above results. Moreover, we do not impose the restricted condition on p(x) and the uniform monotonicity of the operator to show the existence of three distinct solutions.展开更多
In this paper,we mainly discuss a priori bounds of the following degenerate elliptic equation,a^ ij(x)δij u+b^ i(x)δiu+f(x,u)=0,in Ω belong to belong toR^n,(*)where a^ijδiφδjφ=0 on δΩ,andφis the d...In this paper,we mainly discuss a priori bounds of the following degenerate elliptic equation,a^ ij(x)δij u+b^ i(x)δiu+f(x,u)=0,in Ω belong to belong toR^n,(*)where a^ijδiφδjφ=0 on δΩ,andφis the defining function of δΩ.Imposing suitable conditions on the coefficients and f(x,u),one can get the L^∞-estimates of(*)via blow up method.展开更多
基金The National Natural Science Foundation of China(No.60443007,50390063).
文摘A principal component analysis-cerebellar model articulation controller (PCA-CMAC) model is proposed for machine performance degradation assessment.PCA is used to feature selection,which eliminates the redundant information among the features from the sensor signals and reduces the dimension of the input to CMAC.CMAC is used to assess degradation states quantitatively based on its local generalization ability.The implementation of the model is presented and the model is applied in a drilling machine to assess the states of the cutting tool. The results show that the model can assess the wear states quantitatively based on the normal state of the cutting tool.The influence of the quantization parameter g and the generalization parameter r in the CMAC model on the assessment results is analyzed.If g is larger,the generalization ability is better,but the difference of degradation states is not obvious.If r is smaller,the different states are distinct,but memory requirements for storing the weights are larger.The principle for selecting two parameters is that the memory storing the weights should be small while the degradation states should be easily distinguished.
基金Project(Z132012) supported by the Second Five Technology-based Fund in Science and Industry Bureau of ChinaProject(1004GK0032) supported by General Armament Department for the Common Issues of Military Electronic Components,China
文摘A lifetime prediction method for high-reliability tantalum (Ta) capacitors was proposed, based on multiple degradation measures and grey model (GM). For analyzing performance degradation data, a two-parameter model based on GM was developed. In order to improve the prediction accuracy of the two-parameter model, parameter selection based on particle swarm optimization (PSO) was used. Then, the new PSO-GM(1, 2, co) optimization model was constructed, which was validated experimentally by conducting an accelerated testing on the Ta capacitors. The experiments were conducted at three different stress levels of 85, 120, and 145℃. The results of two experiments were used in estimating the parameters. And the reliability of the Ta capacitors was estimated at the same stress conditions of the third experiment. The results indicate that the proposed method is valid and accurate.
文摘This paper deals with positive solutions of a degenerate parabolic system: u t= Δ u m+ v p ln α(h+u), v t= Δ v n+u q ln β(h+v) with homogeneous Dirichlet boundary conditions and positive initial conditions. This system describes the processes of diffusion of heat and burning in two component continuous media with nonlinear conductivity and volume energy release. We obtain the global existence and blow up results of the solution relying on comparison with carefully constructed upper solutions and lower solutions.
基金Supported by the National Natural Science Foundation of China(61172073)Program for New Century Excellent Talents of the Ministry of Education(NCET-12-0766)+1 种基金the Open Research Fund of National Mobile Communications Research Laboratory,Southeast University(2012D19)the Fundamental Research Funds for the Central Universities(2013JBZ001)
文摘A modified random walk model for human motion is proposed to investigate characteristics of 60GHz indoor office propagation.Compared with the classic random walk model,the movement tendency in the walking process is taken into account in the modified model.Based on the proposed model,path gains of the propagation environment are simulated under a variety of settings by using a ray tracing method.Simulation results and analysis show that human motion is a major source of disturbance to the indoor office propagation and results in performance degradation in some areas.
文摘This paper studies the conditions of blow up in finite time of solutions of initial boundary value problem for a class nonlinear doubly degenerate parabolic equation.
基金Supported by the NSSFC(02BTJ001) Supported by the NSSFC(04BTJ002) Supported by the Grant for Post-Doctorial Fellows in Southeast University
文摘This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988)[1.2] and Seber & Wild (1989)[3].
基金Supported by the NNSF of China(10441002)Supported by NNSF of Henan Province(200510466011)
文摘In this paper we study the decay estimate of global solutions to the initial-boundary value problem for double degenerate nonlinear parabolic equation by using a dif-ference inequality.
基金Project supported by the Second Stage of Brain Korea 21 Projects and Changwon National University in 2011-2012
文摘A design and verification of linear state observers which estimate state information such as angular velocity and load torque for retraction control of the motorized seat belt (MSB) system were described. The motorized seat belt system provides functions to protect passengers and improve passenger's convenience. Each MSB function has its own required belt tension which is determined by the function's purpose. To realize the MSB functions, state information, such as seat belt winding velocity and seat belt tension are required. Using a linear state observer, the state information for MSB operations can be estimated without sensors. To design the linear state observer, the motorized seat belt system is analyzed and represented as a state space model which contains load torque as an augmented state. Based on the state space model, a linear state observer was designed and verified by experiments. Also, the retraction control of the MSB algorithm using linear state observer was designed and verified on the test bench. With the designed retraction control algorithm using the linear state observer, it is possible to realize various types of MSB functions.
基金Project supported by the National Natural Science Foundation of China (No. 69673044) the Environmental Protection Bureau of Hangzhou (No. 9901), China
文摘This research considers the mathematical relationship between concentration of Chla and seven environmental factors, i.e. Lake water temperature (T), Secci-depth (SD), pH, DO, CODMn, Total Nitrogen (TN), Total Phosphorus (TP). Stepwise linear regression of 1997 to 1999 monitoring data at each sampling point of Qiandaohu Lake yielded the multivariate regression models presented in this paper. The concentration of Chla as simulation for the year 2000 by the regression model was similar to the observed value. The suggested mathematical relationship could be used to predict changes in the lakewater environment at any point in time. The results showed that SD, TP and pH were the most significant factors affecting Chla concentration.
文摘The mathematic model of heating chamber for implementing the prediction of the annealing craft and improving the self adapting with the expansion of the new annealing furnace form, new annealing crafts and new kinds of steel coil has been established. The model developed which including the temperature for gas in heating chamber and the heating cover is based on the characteristics of anneal craft and the situations of locale production run. Firstly, the characteristic of the heating cover which limits the temperature was considered. Secondly, the locale production run condition and dispatching condition were considered. Finally, combining with the models and the simulation system, the numerical simulation research of the anneal process for the high performance hydrogen bell-type annealer as well as the spot experiment test were carried out. The results obtained from the developed models, usually finished less than thirty seconds, are in fair agreement with the test values, such as the relative errors of annealing times were within ±5%, and the quality' of the annealed steels were guaranteed.
基金supported by National Natural Science Foundation of China (No. 30271502)
文摘Objective It has been reported that D-galactose (D-gal) can model subacute aging, and aluminum (AI) acts as a neurotoxin, but combined effects of them have not been reported. The present work aimed to reveal the effect of combined administration of D-gal and A1 in mice and compare the effect of D-gal treatment with that of A1 treatment. Meth- ods A1 was intragastricaHy administered and D-gal was subcutaneously injected into Kunming mice for 10 consecutive weeks. Learning and memory, eholinergic systems, as well as protein levels of amyloid β (Aβ) and hyperphosphorylated tau were determined using Morri water maze test, biochemical assays and immunohistochemical staining, respectively. Results The mice with combined treatment had obvious learning and memory deficits, and showed decreases in brain ace- tylcholine (ACh) level and in activities of choline acetyltransferase (CHAT) and acetyleholinesterase (ACHE). Formation of senile plaque (SP)-like and neurofibrillary tangle (NFT)-like structures was also observed. The behavioral and pathologi- cal changes persisted for at least 6 weeks after withdrawal of D-gal and A1. Conclusion Combined use of D-gal and A1 is an effective way to establish the non-transgenic Alzheimer's disease (AD) animal model, and is useful for studies of AD pathogenesis and therapeutic evaluation.
基金supported by the grants from the National Natural Science Foundation of China(No.30600197)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20050285017)
文摘Polyglutamine (polyQ) diseases are a family of neurodegenerative disorders including Huntington’s disease, spinobulbar muscular atrophy,dentatorubral-pallidoluysian atrophy and several spinocerebellar ataxias.polyQ diseases are caused by abnormal expansion of CAG repeats in certain genes.The expanded CAG repeats are then translated into a series of abnormally expanded polyQ tracts.Such polyQ tracts may induce misfolding of the disease-causing proteins.The present review mainly focuses on the common characteristics of the pathogenesis of these polyQ diseases,including conformational transition of proteins and its influence on the function of these proteins,the correlation between decreased ability of proteoly-sis and late-onset polyQ diseases,and the relationship between wide expression of disease-causing proteins and selective neuronal death.
基金CHEN Min's work is supported by Grant No. 70221001 and No. 70331001 from NNSFC and Grant No. KZCX2-SW-118 from CAS.
文摘Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is contained in R are fixed design points, β =(β_1,β_2,···,β_p)′ is an unknown parameter vector, g(·) is an unknown bounded real-valuedfunction defined on a compact subset T of the real line R, and ε_k is a linear process given byε_k = ∑ from j=0 to ∞ of ψ_je_(k-j), ψ_0=1, where ∑ from j=0 to ∞ of |ψ_j| < ∞, and e_j,j=0, +-1, +-2,···, ard i.i.d. random variables. In this paper we establish the asymptoticnormality of the least squares estimator of β, a smooth estimator of g(·), and estimators of theautocovariance and autocorrelation functions of the linear process ε_k.
基金Project supported by the National Natural Science Foundation of China
文摘The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with "slow" decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the life-span of classical solutions are given in the case that the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.1-1.3 in [2] are still valid for this kind of initial data.
基金the National Natural Science Foundation of China(No.10131050).
文摘This paper considers the pointwise estimate of the solutions to Cauchy problem for quasilin-ear hyperbolic systems, which bases on the existence of the solutions by using the fundamental solutions. It gives a sharp pointwise estimates of the solutions on domam under consideration. Specially, the estimate is precise near each characteristic direction.
基金supported by National Natural Science Foundation of China (Grant Nos. 10901112, 11001255)Beijing Natural Science Foundation (Grant No. 1102013)China Postdoctoral Science Foundation (Grant No. 20090460548)
文摘In this paper, we study the following degenerate critical elliptic equation with anisotropic coefficients-div(|x N | 2α▽u) = K(x)|x N | α·2 * (s)-s |u| 2 * (s)-2 u in R N ,where x = (x 1 , . . . , x N ) ∈ R N , N≥3, α > 1/2, 0≤ s ≤2 and 2 * (s) = 2(N-s)/(N-2). Some basic properties of the degenerate elliptic operator -div(|x N |2α▽u) are investigated and some regularity, symmetry and uniqueness results for entire solutions of this equation are obtained. We also get some variational identities for solutions of this equation. As consequences, we obtain some nonexistence results for this equation.
基金Project supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE(No.[2000]26)the 973 Project of the Ministry of Science and Technology of China(No.2006CB805902)+1 种基金the National Natural Science Foundation of China(No.10571072)the Key Laboratory of Symbolic Computation and Knowledge Engineering of the Ministry of Education of China and the 985 Project of Jilin University.
文摘The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form: μt-△φ(μ) = 0 ,where φ ε C1(R^1) is a strictly monotone increasing function. Clearly, the above equation has strong degeneracy, i.e., the set of zero points of φ'(.) is permitted to have zero measure. This is an answer to an open problem in [13, p. 288].
基金supported by the National Research Foundation of Korea Grant Funded by the Korea Government (Grant No. NRF-2015R1D1A3A01019789)
文摘We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniqueness and nonnegativeness of solutions when the principal operator is monotone and the nonlinearity is nonincreasing. Our operator is of the most general form containing all previous ones and we also weaken assumptions on the operator and the nonlinearity to get the above results. Moreover, we do not impose the restricted condition on p(x) and the uniform monotonicity of the operator to show the existence of three distinct solutions.
基金supported by National Natural Science Foundation of China(Grant No.11131005)
文摘In this paper,we mainly discuss a priori bounds of the following degenerate elliptic equation,a^ ij(x)δij u+b^ i(x)δiu+f(x,u)=0,in Ω belong to belong toR^n,(*)where a^ijδiφδjφ=0 on δΩ,andφis the defining function of δΩ.Imposing suitable conditions on the coefficients and f(x,u),one can get the L^∞-estimates of(*)via blow up method.