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Simulation of Quasi-Linear Mesoscale Convective Systems in Northern China:Lightning Activities and Storm Structure 被引量:7
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作者 Wanli LI Xiushu QIE +2 位作者 Shenming FU Debin SU Yonghai SHEN 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2016年第1期85-100,共16页
Two intense quasi-linear mesoscale convective systems(QLMCSs) in northern China were simulated using the WRF(Weather Research and Forecasting) model and the 3D-Var(three-dimensional variational) analysis system ... Two intense quasi-linear mesoscale convective systems(QLMCSs) in northern China were simulated using the WRF(Weather Research and Forecasting) model and the 3D-Var(three-dimensional variational) analysis system of the ARPS(Advanced Regional Prediction System) model.A new method in which the lightning density is calculated using both the precipitation and non-precipitation ice mass was developed to reveal the relationship between the lightning activities and QLMCS structures.Results indicate that,compared with calculating the results using two previous methods,the lightning density calculated using the new method presented in this study is in better accordance with observations.Based on the calculated lightning densities using the new method,it was found that most lightning activity was initiated on the right side and at the front of the QLMCSs,where the surface wind field converged intensely.The CAPE was much stronger ahead of the southeastward progressing QLMCS than to the back it,and their lightning events mainly occurred in regions with a large gradient of CAPE.Comparisons between lightning and non-lightning regions indicated that lightning regions featured more intense ascending motion than non-lightning regions;the vertical ranges of maximum reflectivity between lightning and non-lightning regions were very different;and the ice mixing ratio featured no significant differences between the lightning and non-lightning regions. 展开更多
关键词 quasi-linear mesoscale convective system Weather Research and Forecasting model Advanced Regional Prediction System model precipitation and non-precipitation ice
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MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF QUASI-LINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENT 被引量:4
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作者 范海宁 刘晓春 《Acta Mathematica Scientia》 SCIE CSCD 2014年第4期1111-1126,共16页
In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we ... In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions. 展开更多
关键词 Nehari manifold critical Sobolev exponent quasi-linear problem mini-max principle multiple positive solutions
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Symmetry Reductions of Cauchy Problems for Fourth-Order Quasi-Linear Parabolic Equations 被引量:2
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作者 李吉娜 张顺利 苏敬蕊 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第1期28-36,共9页
This paper is devoted to studying symmetry reduction of Cauchy problems for the fourth-order quasi-linear parabolic equations that admit certain generalized conditional symmetries (GCSs). Complete group classificati... This paper is devoted to studying symmetry reduction of Cauchy problems for the fourth-order quasi-linear parabolic equations that admit certain generalized conditional symmetries (GCSs). Complete group classification results are presented, and some examples are given to show the main reduction procedure. 展开更多
关键词 fourth-order quasi-linear parabolic equation symmetry reduction Cauchy problem
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Solutions and Conditional Lie-Backlund Symmetries of Quasi-linear Diffusion-Reaction Equations 被引量:1
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作者 ZUO Su-Li QU Chang-Zheng 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第1期6-12,共7页
New classes of exact solutions of the quasi-linear diffusion-reaction equations are obtained by seeking for the high-order conditional Lie-Baeklund symmetries of the considered equations. The method used here extends ... New classes of exact solutions of the quasi-linear diffusion-reaction equations are obtained by seeking for the high-order conditional Lie-Baeklund symmetries of the considered equations. The method used here extends the approaches of derivative-dependent functional separation of variables and the invariant subspace. Behavior to some solutions such as blow-up and quenching is also described. 展开更多
关键词 conditional Lie-Backlund symmetry exact solution quasi-linear diffusion-reaction equation
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Entropy generation analysis of tangent hyperbolic fluid in quadratic Boussinesq approximation using spectral quasi-linearization method 被引量:1
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作者 C.SRINIVAS REDDY B.MAHANTHESH +1 位作者 P.RANA K.S.NISAR 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2021年第10期1525-1542,共18页
In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense importance in technology,engineering,and science.These processe... In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense importance in technology,engineering,and science.These processes are relevant for polymer solutions,porous industrial materials,ceramic processing,oil recovery,and fluid beds.The present tangent hyperbolic fluid flow and heat transfer model accurately predicts the shear-thinning phenomenon and describes the blood flow characteristics.Therefore,the entropy production analysis of a non-Newtonian tangent hyperbolic material flow through a vertical microchannel with a quadratic density temperature fluctuation(quadratic/nonlinear Boussinesq approximation)is performed in the present study.The impacts of the hydrodynamic flow and Newton’s thermal conditions on the flow,heat transfer,and entropy generation are analyzed.The governing nonlinear equations are solved with the spectral quasi-linearization method(SQLM).The obtained results are compared with those calculated with a finite element method and the bvp4c routine.In addition,the effects of key parameters on the velocity of the hyperbolic tangent material,the entropy generation,the temperature,and the Nusselt number are discussed.The entropy generation increases with the buoyancy force,the pressure gradient factor,the non-linear convection,and the Eckert number.The non-Newtonian fluid factor improves the magnitude of the velocity field.The power-law index of the hyperbolic fluid and the Weissenberg number are found to be favorable for increasing the temperature field.The buoyancy force caused by the nonlinear change in the fluid density versus temperature improves the thermal energy of the system. 展开更多
关键词 tangent hyperbolic fluid nonlinear Boussinesq approximation entropy production convective boundary condition spectral quasi-linearization method(SQLM)
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A Robin Problem for Quasi-linear System 被引量:1
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作者 0UYANGCheng 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第2期160-163,共4页
In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using... In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using the theory of differential inequalities. 展开更多
关键词 quasi-linear system Robin problem singular perturbation differential inequalities
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A PRIORI ESTIMATE FOR MAXIMUM MODULUS OF GENERALIZED SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS 被引量:1
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作者 梁延 王向东 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第10期941-953,共13页
Let G he a hounded domain in E Consider the following quasi-linear elliptic equationAlthough the houndedness of generalized solutions of the equation is proved for very general structural conditions, it does not suppl... Let G he a hounded domain in E Consider the following quasi-linear elliptic equationAlthough the houndedness of generalized solutions of the equation is proved for very general structural conditions, it does not supply a priori estimate for maximum modulus of solutions. In this paper an estimate to the maximum modulus is made firstly for a special case of quasi-linear elliptic equations, i.e. the A and B satisfy the following structural conditions 展开更多
关键词 quasi-linear elliptic equations generalized solutions maximum modulus a priori estimate.
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Global Smooth Solution for the Quasi-linear Wave Equation 被引量:1
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作者 SONG Chang-ruing JIANG Shi-jing 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2005年第3期269-279,共11页
In this paper, we study the Cauchy problem for the following quasi-linear wave equation utt-2kuxxt=β(ux^n)x, where k〉0 and β are real numbers, and n ≥ 2 is an integer. We prove that for any T〉0, the Cauchy prob... In this paper, we study the Cauchy problem for the following quasi-linear wave equation utt-2kuxxt=β(ux^n)x, where k〉0 and β are real numbers, and n ≥ 2 is an integer. We prove that for any T〉0, the Cauchy problem admits a unique global smooth solution u∈C^∞((0, T]; H^∞(R)) ∩ C([0, T]; H^2(R)) ∩ C^1([0, T]; L^2(R)) under suitable assumptions on the initial data. 展开更多
关键词 quasi-linear wave equation Cauchy problem global smooth solution
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EXISTENCE OF POSITIVE SOLUTIONS TO QUASI-LINEAR EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENT
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作者 康东升 《Acta Mathematica Scientia》 SCIE CSCD 2004年第4期639-644,共6页
This paper is concerned with the quasi-linear equation with critical Sobolev-Hardy exponent whereΩ(?)RN(N(?)3)is a smooth bounded domain,0∈Ω,0(?)s<p,1<p<N,p(s):=p(N-s)/N-p is the critical Sobolev-Hardy exp... This paper is concerned with the quasi-linear equation with critical Sobolev-Hardy exponent whereΩ(?)RN(N(?)3)is a smooth bounded domain,0∈Ω,0(?)s<p,1<p<N,p(s):=p(N-s)/N-p is the critical Sobolev-Hardy exponent,λ>0,p(?)r<p,p:=Np/N-p is the critical Sobolev exponent,μ>,0(?)t<p,p(?)q<p(t)=p(N-t)/N-p.The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method. 展开更多
关键词 Positive solution quasi-linear equation critical Sobolev-Hardy exponent variational method
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THE ESTIMATION OF SOLUTION OF THE BOUNDARY VALUE PROBLEM OF THE SYSTEMS FOR QUASI-LINEAR ORDINARY DIFFERENTIAL EQUATIONS
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作者 黄蔚章 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1992年第8期745-754,共10页
This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix ... This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix function. Under suitable conditions we prove the existence of the solutions by diagonalization and the fixed point theorem and also estimate the remainder. 展开更多
关键词 systems of the quasi-linear ordinary differential equation singular perturbation DIAGONALIZATION asymptotic expansion
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Analysis of Singularity for Reducible Quasi-linear Hyperbolic Systems
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作者 WANGLi-zhen 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2005年第1期10-20,共11页
In this paper we investigate the formation of singularities of hyperbolic systems.Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of cl... In this paper we investigate the formation of singularities of hyperbolic systems.Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of classic solutions is due to the envelope of characteristics of the same family, analyze the geometric properties of the envelope of characteristics and estimate the blowup rates of the solution precisely. 展开更多
关键词 quasi-linear systems strictly hyperbolic systems life span blowup of cusp type the envelope of characteristics
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Boundary Value Problems of Quasi-linear Ordinary Differential Equations on the Semi-infinite Interval
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作者 YANG Hui-sheng MA Yun-xin 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第3期331-337,共7页
Existence of positive solution is established for boundary value problems of nonsingular for a class quasi-linear ordinary differential equation on the semi-infinite interval. The results are obtained by using the non... Existence of positive solution is established for boundary value problems of nonsingular for a class quasi-linear ordinary differential equation on the semi-infinite interval. The results are obtained by using the nonlinear alternative of Leray-Schauder method. 展开更多
关键词 positive solution quasi-linear ordinary differential equation EXISTENCE
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THE INITIAL BOUNDARY VALUE PROBLEM FOR QUASI-LINEAR SCHRODINGER-POISSON EQUATIONS
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作者 郝成春 《Acta Mathematica Scientia》 SCIE CSCD 2006年第1期115-124,共10页
In this article, the author studies the iuitial (Dirichlet.) boundary problem for a high field version of the Schroedinger-Poisson equations, which include a nonlinear term in the Poisson equation corresponding to a... In this article, the author studies the iuitial (Dirichlet.) boundary problem for a high field version of the Schroedinger-Poisson equations, which include a nonlinear term in the Poisson equation corresponding to a field-dependent dielectric constant and an effective potential in the Schroedinger equations on the unit cube. h global existence and uniqueness is established for a solution to this problem. 展开更多
关键词 quasi-linear Schroedinger-Poisson system Dirichlet boundary conditions global existence and uniqueness
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Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source
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作者 吉飞宇 杨春晓 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第10期67-72,共6页
By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = (A(u)Ux)x + eB(u, Ux). A complete classification of t... By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = (A(u)Ux)x + eB(u, Ux). A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples. 展开更多
关键词 quasi-linear diffusion equation approximate derivative-dependent functional separable solution approximate generalized conditional symmetry
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An O(k<sup>2</sup>+kh<sup>2</sup>+h<sup>2</sup>) Accurate Two-level Implicit Cubic Spline Method for One Space Dimensional Quasi-linear Parabolic Equations
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作者 Ranjan Kumar Mohanty Vijay Dahiya 《American Journal of Computational Mathematics》 2011年第1期11-17,共7页
In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate init... In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline approximation produces at each time level a spline function which may be used to obtain the solution at any point in the range of the space variable. The proposed cubic spline method is applicable to parabolic equations having singularity. The stability analysis for diffusion- convection equation shows the unconditionally stable character of the cubic spline method. The numerical tests are performed and comparative results are provided to illustrate the usefulness of the proposed method. 展开更多
关键词 quasi-linear Parabolic EQUATION IMPLICIT METHOD Cubic Spline Approximation Diffusion-Convection EQUATION Singular EQUATION Burgers’ EQUATION Reynolds Number
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L^(p)Solution of Reflected BSDEs with One Continuous Barrier and Quasi-linear Growth Generators
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作者 Sheng-jun FAN 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2024年第4期943-953,共11页
This paper is devoted to solving a reflected backward stochastic differential equation(BSDE in short)with one continuous barrier and a quasi-linear growth generator g,which has a linear growth in(y,z),except the upper... This paper is devoted to solving a reflected backward stochastic differential equation(BSDE in short)with one continuous barrier and a quasi-linear growth generator g,which has a linear growth in(y,z),except the upper direction in case of y<0,and is more general than the usual linear growth generator.By showing the convergence of a penalization scheme we prove existence and comparison theorem of the minimal L^(p)(p>1)solutions for the reflected BSDEs.We also prove that the minimal Lpsolution can be approximated by a sequence of Lpsolutions of certain reflected BSDEs with Lipschitz generators. 展开更多
关键词 Reflected BSDEs quasi-linear growth L^(p)solution EXISTENCE Comparison theorem
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Infinitely Many Solutions for a Class of Quasi-linear Elliptic Problem
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作者 Xiao-yao JIA Zhen-luo LOU 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2024年第3期728-743,共16页
In this paper,we study the following quasi-linear elliptic equation:■where Ω?R^(N) is a bounded domain,λ>0 is a parameter.The function ψ(|t|)t is the subcritical term,and φ(|t|)t is the critical Orlicz-Sobolev... In this paper,we study the following quasi-linear elliptic equation:■where Ω?R^(N) is a bounded domain,λ>0 is a parameter.The function ψ(|t|)t is the subcritical term,and φ(|t|)t is the critical Orlicz-Sobolev growth term with respect to φ.Under appropriate conditions on φ,ψ and φ,we prove the existence of infinitely many weak solutions for quasi-linear elliptic equation,for λ∈(0,λ_(0)),where λ_(0)> 0 is a fixed constant. 展开更多
关键词 quasi-linear elliptic equations variational methods Orlicz-Sobolev spaces
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Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm
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作者 Alexey Shcheglov Jingzhi Li +2 位作者 Chao Wang Alexander Ilin Ye Zhang 《Advances in Applied Mathematics and Mechanics》 SCIE 2024年第1期237-252,共16页
This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations(PDEs).Using the integral equation method,we prove the uniqueness of the inverse probl... This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations(PDEs).Using the integral equation method,we prove the uniqueness of the inverse problem in nonlinear PDEs.Moreover,using the method of successive approximations,we develop a novel iterative algorithm to estimate sorption isotherms.The stability results of the algorithm are proven under both a priori and a posteriori stopping rules.A numerical example is given to show the efficiency and robustness of the proposed new approach. 展开更多
关键词 Inverse problem quasi-linear dynamic model UNIQUENESS method of successive approximations stability
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Decoupling Analysis for a Powertrain Mounting System with a Combination of Hydraulic Mounts 被引量:7
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作者 HU Jinfang CHEN Wuwei HUANG He 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2013年第4期737-745,共9页
The existing torque roll axis(TRA) decoupling theories for a powertrain mounting system assume that the stiffness and viscous damping properties are constant. However, real-life mounts exhibit considerable spectrally ... The existing torque roll axis(TRA) decoupling theories for a powertrain mounting system assume that the stiffness and viscous damping properties are constant. However, real-life mounts exhibit considerable spectrally varying stiffness and damping characteristics, and the influence of the spectrally-varying properties of the hydraulic mounts on the powertrain system cannot be ignored. To overcome the deficiency, an analytical quasi-linear model of the hydraulic mount and the coupled properties of the powertrain and hydraulic mounts system are formulated. The influence of the hydraulic mounts on the TRA decoupling of a powertrain system is analytically examined in terms of eigensolutions, frequency, and impulse responses, and then a new analytical axiom is proposed based on the TRA decoupling indices. With the experimental setup of a fixed decoupler hydraulic mount in the context of non-resonant dynamic stiffness testing procedure, the quasi-linear model of the hydraulic mount is verified by comparing the predictions with the measurement. And the quasi-linear formulation of the coupled system is also verified by comparing the frequency responses with the numerical results obtained by the direct inversion method. Finally, the mounting system with a combination of hydraulic mounts is redesigned in terms of the stiffness, damping and mount locations by satisfying the new axiom. The frequency and time domain results of the redesigned system demonstrate that the torque roll axis of the redesigned powertrain mounting system is indeed decoupled in the presence of hydraulic mounts (given oscillating torque or impulsive torque excitation). The proposed research provides an important basis and method for the research on a powertrain system with spectrally-varying mount properties, especially for the TRA decoupling. 展开更多
关键词 hydraulic mount coupled quasi-linear system motion control TRA decoupling
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BLOW-UP ESTIMATES FOR A NON-NEWTONIAN FILTRATION SYSTEM 被引量:3
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作者 YANG Zuo-dong(杨作东) +1 位作者 LU Qi-shao(陆启韶) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第3期332-339,共8页
The prior estimate and decay property of positive solutions are derived for a system of quasi- linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radia... The prior estimate and decay property of positive solutions are derived for a system of quasi- linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blowup estimates for a class quasi-linear reaction-diffusion systems ( non-Newtonian filtration systems) are established, which extends the result of semi-linear reaction diffusion( Fujita type) systems. 展开更多
关键词 BLOW-UP blow-up rates quasi-linear equation system
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