We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
We consider a class of doubly nonlinear history-dependent problems having a convection term and a pseudomonotone nonlinear diffusion operator associated an equation of the type ?<sub>t</sub>(k * (b(v) - b(...We consider a class of doubly nonlinear history-dependent problems having a convection term and a pseudomonotone nonlinear diffusion operator associated an equation of the type ?<sub>t</sub>(k * (b(v) - b(v<sub>0</sub>))) - div(a(x,Dv) + F(v)) = f where the right hand side belongs to L<sup>1</sup>. The kernel k belongs to the large class of PC kernels. In particular, the case of fractional time derivatives of order α ∈ (0,1) is included. Assuming b nondecreasing with L<sup>1</sup>-data, we prove existence in the framework of entropy solutions. The approach adopted for the proof is based on a several step approximation method and by using a result in the case of a strictly increasing b.展开更多
We study the existence and uniqueness problem for the nonhomogeneous pressureless Euler system with the initial density being a Radon measure. Our uniqueness result is obtained in the same space as the existence theor...We study the existence and uniqueness problem for the nonhomogeneous pressureless Euler system with the initial density being a Radon measure. Our uniqueness result is obtained in the same space as the existence theorem. Besides, by counterexample we prove that Huang-Wang’s energy condition is also necessary for our nonhomogeneous system.展开更多
We give an existence result of the obstacle parabolic equations3b(x,u) div(a(x,t,u, Vu))+div((x,t,u))=f in QT, 3twhere b(x,u) is bounded function ot u, the term atva,x,r,u, v u)) is a Letay type operat...We give an existence result of the obstacle parabolic equations3b(x,u) div(a(x,t,u, Vu))+div((x,t,u))=f in QT, 3twhere b(x,u) is bounded function ot u, the term atva,x,r,u, v u)) is a Letay type operator and the function is a nonlinear lower order and satisfy only the growth condition. The second term belongs to L1 (QT). The proof of an existence solution is based on the penalization methods.展开更多
In this paper we consider one dimensional mean-field backward stochastic differential equations(BSDEs)under weak assumptions on the coefficient.Unlike[3],the generator of our mean-field BSDEs depends not only on the s...In this paper we consider one dimensional mean-field backward stochastic differential equations(BSDEs)under weak assumptions on the coefficient.Unlike[3],the generator of our mean-field BSDEs depends not only on the solution(Y,Z)but also on the law PY of Y.The first part of the paper is devoted to the existence and uniqueness of solutions in Lp,1<p≤2,where the monotonicity conditions are satisfied.Next,we show that if the generator/is uniformly continuous in(μ,y,z),uniformly with respect to(t,ω) and if the terminal valueξbelongs to Lp(Ω,F,P)with 1<p≤2,the mean-field BSDE has a unique Lp solution.展开更多
We are concerned with the uniqueness of solutions of the Cauchy problemand a(s),b(s) are appropriately smooth.Since a(s) is allowed to have zero points, we call them points of degeneracy of (1), the equation (1) does ...We are concerned with the uniqueness of solutions of the Cauchy problemand a(s),b(s) are appropriately smooth.Since a(s) is allowed to have zero points, we call them points of degeneracy of (1), the equation (1) does not admit classical solutions in general. The solutions of (1) even might be discontinuous, whenever the set E = {s : a(s) = 0} includes interior points.Equations with degeneracy arise from a wide variety of diffusive processes in nature展开更多
We derive the entropy functions whose local equilibria are suitable to recover the Euler-like equations in the framework of the lattice Boltzmann method. Numerical examples are also given, which are consistent with th...We derive the entropy functions whose local equilibria are suitable to recover the Euler-like equations in the framework of the lattice Boltzmann method. Numerical examples are also given, which are consistent with the above theoretical arguments. In all cases, we observe a negative entropy range existing near the shock, while numerical oscillations are captured.展开更多
Let f be a continuous anti-unimodal solution of a p-order Frigenbaum's dunctioal equation.A criterion is given to determine whether or not the topological entropy of j is zero.And a continuous anti-unimodal soluti...Let f be a continuous anti-unimodal solution of a p-order Frigenbaum's dunctioal equation.A criterion is given to determine whether or not the topological entropy of j is zero.And a continuous anti-unimodal solution of 4-order equation with positive topological eotrpy is constructed.展开更多
We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics...We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ(T ) is assumed to have a positive lower bound. We first consider the Cauchy problem (the initial value problem), that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave (weak or strong, determined by the wedge angle at the wedge vertex) when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.展开更多
This paper is concerned with the initial-boundary value problem of scalar conservation laws with weak discontinuous flux, whose initial data are a function with two pieces of constant and whose boundary data are a con...This paper is concerned with the initial-boundary value problem of scalar conservation laws with weak discontinuous flux, whose initial data are a function with two pieces of constant and whose boundary data are a constant function. Under the condition that the flux function has a finite number of weak discontinuous points, by using the structure of weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux-Nedelec, we give a construction method to the global weak entropy solution for this initial-boundary value problem, and by investigating the interaction of elementary waves and the boundary, we clarify the geometric structure and the behavior of boundary for the weak entropy solution.展开更多
This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standar...This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standard iteration technique, then we deduce the basic energy estimate by constructing a convex entropy-entropy flux pair to this system. Moreover, the L∞-estimates and H^2-estimates of solutions are obtained through some delicate estimates. In our results, we do not ask the far fields of the initial data to be equal and the initial data can be arbitrarily large which generalize the result obtained in [7].展开更多
MCoCrFeNiTix (M = Cu, Al; x: molar ratio, x = 0, 0.5) alloys were prepared using the new alloy-design strategy of equal-atomic ratio and high entropy. By the component substitution orAl for Cu, the microstructure c...MCoCrFeNiTix (M = Cu, Al; x: molar ratio, x = 0, 0.5) alloys were prepared using the new alloy-design strategy of equal-atomic ratio and high entropy. By the component substitution orAl for Cu, the microstructure changes from the face-centered cubic solid solution of original CuCoCrFeNiTix alloys to the body-centered cubic solid solution of AlCoCrFeNiTix alloys. Compared with original CuCoCrFeNiTix alloys, AlCoCrFeNiTix alloys keep the similar good ductility and simultaneously possess a much higher compressive strength, which are even superior to most of the reported high-strength alloys like bulk metallic glasses.展开更多
The statistical counting method for the computer simulation of the thermodynamic quantities of polymer solution has been reviewed. The calculating results for a single athermal chain confirm the theory of the renorma...The statistical counting method for the computer simulation of the thermodynamic quantities of polymer solution has been reviewed. The calculating results for a single athermal chain confirm the theory of the renormalization group. The results for the athermal solution are consistent with the scaling law of the osmotic pressure with the exponent 2.25. The results for a single chain with the segmental interaction are in a good agreement with the exact results obtained by the direct counting method. The results for the polymer solution show us that the Flory-Huggins parameter is strongly dependent on both the polymer concentration and the interaction energy between segments. (Author abstract) 15 Refs.展开更多
Using finite differences and entropy inequalities, the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained. The nonnegativity of the solutions is also sh...Using finite differences and entropy inequalities, the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained. The nonnegativity of the solutions is also shown.展开更多
In this paper, we show the existence of the renormalized solutions and the entropy solutions of a class of strongly degenerate quasilinear parabolic equations.
This paper is concerned with the initial-boundary value problem of a nonlinear conservation law in the half space R+= {x |x > 0} where a>0 , u(x,t) is an unknown function of x ∈ R+ and t>0 , u ± , um ar...This paper is concerned with the initial-boundary value problem of a nonlinear conservation law in the half space R+= {x |x > 0} where a>0 , u(x,t) is an unknown function of x ∈ R+ and t>0 , u ± , um are three given constants satisfying um=u+≠u- or um=u-≠u+ , and the flux function f is a given continuous function with a weak discontinuous point ud. The main purpose of our present manuscript is devoted to studying the structure of the global weak entropy solution for the above initial-boundary value problem under the condition of f '-(ud) > f '+(ud). By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial-boundary value problem, and investigate the interaction of elementary waves with the boundary and the boundary behavior of the weak entropy solution.展开更多
In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate pa...In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.展开更多
目的采用一测多评(QAMS)法同时测定法制半夏曲中肌苷、鸟苷、腺苷等11种成分含量,并建立其灰色关联度分析(GRA)联合熵权逼近理想解排序分析法(EW-TOPSIS)综合质量评价方法。方法采用Shimadzu C 18色谱柱;乙腈-0.5%醋酸为流动相,梯度洗脱...目的采用一测多评(QAMS)法同时测定法制半夏曲中肌苷、鸟苷、腺苷等11种成分含量,并建立其灰色关联度分析(GRA)联合熵权逼近理想解排序分析法(EW-TOPSIS)综合质量评价方法。方法采用Shimadzu C 18色谱柱;乙腈-0.5%醋酸为流动相,梯度洗脱,流速1.0 mL·min-1;检测波长254和290 nm。以对甲氧基肉桂酸乙酯为内参比物质,计算其他10个成分的相对校正因子(RCF),测定各成分含量。采用GRA联合EW-TOPSIS模型对法制半夏曲进行综合质量评价。结果法制半夏曲中11种成分在一定浓度范围内线性关系良好,相关系数均>0.999;平均加样回收率96.94%~100.12%(RSD<2.0%,n=9);QAMS与外标法(ESM)实测值无明显差异。GRA模型相对关联度0.2903~0.6187,EW-TOPSIS模型相对接近度0.2114~0.6343;GRA和EW-TOPSIS模型综合评价结果基本一致。结论QAMS法便捷、准确,可用于法制半夏曲多指标成分定量控制,GRA联合EW-TOPSIS模型可用于法制半夏曲综合质量评价。展开更多
文摘We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
文摘We consider a class of doubly nonlinear history-dependent problems having a convection term and a pseudomonotone nonlinear diffusion operator associated an equation of the type ?<sub>t</sub>(k * (b(v) - b(v<sub>0</sub>))) - div(a(x,Dv) + F(v)) = f where the right hand side belongs to L<sup>1</sup>. The kernel k belongs to the large class of PC kernels. In particular, the case of fractional time derivatives of order α ∈ (0,1) is included. Assuming b nondecreasing with L<sup>1</sup>-data, we prove existence in the framework of entropy solutions. The approach adopted for the proof is based on a several step approximation method and by using a result in the case of a strictly increasing b.
文摘We study the existence and uniqueness problem for the nonhomogeneous pressureless Euler system with the initial density being a Radon measure. Our uniqueness result is obtained in the same space as the existence theorem. Besides, by counterexample we prove that Huang-Wang’s energy condition is also necessary for our nonhomogeneous system.
文摘We give an existence result of the obstacle parabolic equations3b(x,u) div(a(x,t,u, Vu))+div((x,t,u))=f in QT, 3twhere b(x,u) is bounded function ot u, the term atva,x,r,u, v u)) is a Letay type operator and the function is a nonlinear lower order and satisfy only the growth condition. The second term belongs to L1 (QT). The proof of an existence solution is based on the penalization methods.
基金supported in part by the NSFC(11222110,11871037)Shandong Province(JQ201202)+1 种基金NSFC-RS(11661130148,NA150344)111 Project(B12023)。
文摘In this paper we consider one dimensional mean-field backward stochastic differential equations(BSDEs)under weak assumptions on the coefficient.Unlike[3],the generator of our mean-field BSDEs depends not only on the solution(Y,Z)but also on the law PY of Y.The first part of the paper is devoted to the existence and uniqueness of solutions in Lp,1<p≤2,where the monotonicity conditions are satisfied.Next,we show that if the generator/is uniformly continuous in(μ,y,z),uniformly with respect to(t,ω) and if the terminal valueξbelongs to Lp(Ω,F,P)with 1<p≤2,the mean-field BSDE has a unique Lp solution.
基金Partially supported by NSF (19631050) of China, partially supported by the grant of Ministry of Science and Technologies of China, and partially supported by the Outstanding Young Fundation (19125107) of China.
文摘We are concerned with the uniqueness of solutions of the Cauchy problemand a(s),b(s) are appropriately smooth.Since a(s) is allowed to have zero points, we call them points of degeneracy of (1), the equation (1) does not admit classical solutions in general. The solutions of (1) even might be discontinuous, whenever the set E = {s : a(s) = 0} includes interior points.Equations with degeneracy arise from a wide variety of diffusive processes in nature
基金supported by the National Natural Science Foundation of China(Grant Nos.90816013 and 10572083)
文摘We derive the entropy functions whose local equilibria are suitable to recover the Euler-like equations in the framework of the lattice Boltzmann method. Numerical examples are also given, which are consistent with the above theoretical arguments. In all cases, we observe a negative entropy range existing near the shock, while numerical oscillations are captured.
文摘Let f be a continuous anti-unimodal solution of a p-order Frigenbaum's dunctioal equation.A criterion is given to determine whether or not the topological entropy of j is zero.And a continuous anti-unimodal solution of 4-order equation with positive topological eotrpy is constructed.
基金Gui-Qiang CHEN was supported in part by the UK EPSRC Science and Innovation Award to the Oxford Centre for Nonlinear PDE(EP/E035027/1)the NSFC under a joint project Grant 10728101+4 种基金the Royal Society-Wolfson Research Merit Award(UK)Changguo XIAO was supported in part by the NSFC under a joint project Grant 10728101Yongqian ZHANG was supported in part by NSFC Project 11031001NSFC Project 11121101the 111 Project B08018(China)
文摘We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ(T ) is assumed to have a positive lower bound. We first consider the Cauchy problem (the initial value problem), that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave (weak or strong, determined by the wedge angle at the wedge vertex) when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.
文摘This paper is concerned with the initial-boundary value problem of scalar conservation laws with weak discontinuous flux, whose initial data are a function with two pieces of constant and whose boundary data are a constant function. Under the condition that the flux function has a finite number of weak discontinuous points, by using the structure of weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux-Nedelec, we give a construction method to the global weak entropy solution for this initial-boundary value problem, and by investigating the interaction of elementary waves and the boundary, we clarify the geometric structure and the behavior of boundary for the weak entropy solution.
基金Huijiang Zhao was supported by the National Natural Science Foundation of China (10871151)Changjiang Zhu was supported by the National Natural Science Foundation of China (10625105 and 10431060)the Program for New Century Excellent Talentsin University (NCET-04-0745)
文摘This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standard iteration technique, then we deduce the basic energy estimate by constructing a convex entropy-entropy flux pair to this system. Moreover, the L∞-estimates and H^2-estimates of solutions are obtained through some delicate estimates. In our results, we do not ask the far fields of the initial data to be equal and the initial data can be arbitrarily large which generalize the result obtained in [7].
基金support by the National Natural Science Foundation of China (No. 50571018)the Program for New Century Excellent Talents in Universities of China (No. NCET- 05-0105)
文摘MCoCrFeNiTix (M = Cu, Al; x: molar ratio, x = 0, 0.5) alloys were prepared using the new alloy-design strategy of equal-atomic ratio and high entropy. By the component substitution orAl for Cu, the microstructure changes from the face-centered cubic solid solution of original CuCoCrFeNiTix alloys to the body-centered cubic solid solution of AlCoCrFeNiTix alloys. Compared with original CuCoCrFeNiTix alloys, AlCoCrFeNiTix alloys keep the similar good ductility and simultaneously possess a much higher compressive strength, which are even superior to most of the reported high-strength alloys like bulk metallic glasses.
基金This work was supported by the National Key Project for Fundamental Research"Macromolecular Condensed State",The State Science and Technology Commission of China
文摘The statistical counting method for the computer simulation of the thermodynamic quantities of polymer solution has been reviewed. The calculating results for a single athermal chain confirm the theory of the renormalization group. The results for the athermal solution are consistent with the scaling law of the osmotic pressure with the exponent 2.25. The results for a single chain with the segmental interaction are in a good agreement with the exact results obtained by the direct counting method. The results for the polymer solution show us that the Flory-Huggins parameter is strongly dependent on both the polymer concentration and the interaction energy between segments. (Author abstract) 15 Refs.
基金supported by the National Natural Science Foundation of China (Nos. 10701024, 10601011)
文摘Using finite differences and entropy inequalities, the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained. The nonnegativity of the solutions is also shown.
基金The NSFC (10626024) of ChinaChina Postdoctoral Science Foundation and Graduate Innovation Lab of Jilin University
文摘In this paper, we show the existence of the renormalized solutions and the entropy solutions of a class of strongly degenerate quasilinear parabolic equations.
文摘This paper is concerned with the initial-boundary value problem of a nonlinear conservation law in the half space R+= {x |x > 0} where a>0 , u(x,t) is an unknown function of x ∈ R+ and t>0 , u ± , um are three given constants satisfying um=u+≠u- or um=u-≠u+ , and the flux function f is a given continuous function with a weak discontinuous point ud. The main purpose of our present manuscript is devoted to studying the structure of the global weak entropy solution for the above initial-boundary value problem under the condition of f '-(ud) > f '+(ud). By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial-boundary value problem, and investigate the interaction of elementary waves with the boundary and the boundary behavior of the weak entropy solution.
文摘In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.
文摘目的采用一测多评(QAMS)法同时测定法制半夏曲中肌苷、鸟苷、腺苷等11种成分含量,并建立其灰色关联度分析(GRA)联合熵权逼近理想解排序分析法(EW-TOPSIS)综合质量评价方法。方法采用Shimadzu C 18色谱柱;乙腈-0.5%醋酸为流动相,梯度洗脱,流速1.0 mL·min-1;检测波长254和290 nm。以对甲氧基肉桂酸乙酯为内参比物质,计算其他10个成分的相对校正因子(RCF),测定各成分含量。采用GRA联合EW-TOPSIS模型对法制半夏曲进行综合质量评价。结果法制半夏曲中11种成分在一定浓度范围内线性关系良好,相关系数均>0.999;平均加样回收率96.94%~100.12%(RSD<2.0%,n=9);QAMS与外标法(ESM)实测值无明显差异。GRA模型相对关联度0.2903~0.6187,EW-TOPSIS模型相对接近度0.2114~0.6343;GRA和EW-TOPSIS模型综合评价结果基本一致。结论QAMS法便捷、准确,可用于法制半夏曲多指标成分定量控制,GRA联合EW-TOPSIS模型可用于法制半夏曲综合质量评价。