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Acta Mathematica Scientia 2006年第2期26卷 255-264页

作者：招燕燕陈祖墀 Department of Mathematics University of Science and Technology of China Hefei 230026China

This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotrop... 详细信息

关键词： Weak solution strongly degenerate quasilinear parabolic equation 2000 MR Subject Classification 35k55 35k60 35k65

On the Cauchy problem for a doubly nonlinear degenerate parabolic equation with strongly nonlinear sources

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Science China Mathematics 2008年第11期51卷 2059-2071页

作者： ZHENG TingTing ZHAO JunNing School of Mathematical Sciences Xiamen UniversityXiamen 361005China

In this article, we consider the existence of local and global solution to the Cauchy problem of a doubly nonlinear equation. By introducing the norms |||f||| h and 〈f〉h, we give the sufficient and necessary conditions on the initial value to the existence of local solution of doubly nonlinear equation. Moreover some results on the global existence and nonexistence of solutions are considered.

关键词： degenerate parabolic nonlinear sources global and local solutions 35k65 35k55

Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries

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Science China Mathematics 2007年第9期50卷 1251-1266页

作者： Ling-hua kONG~(1+) Ming-xin WANG~(2,3) 1 Department of Applied Mathematics,Dalian University of Technology,Dalian 116024,China 2 Department of Mathematics,Southeast University,Nanjing 210018,China 3 Department of Mathematics,Xuzhou Normal University,Xuzhou 221116,China Department of Applied Mathematics Dalian University of Technology Dalian China Department of Mathematics Southeast University Nanjing China Department of Mathematics Xuzhou Normal University Xuzhou China

This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. By using super-and sub-solution techniques, we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively, and then give the necessary and sufficient conditions that two components u and ν blow up simultaneously. Finally, the uniform blow-up profiles in the interior are presented.

关键词： parabolic system nonlocal sources nonlocal boundary conditions blow-up set simultaneous blow-up uniform blow-up profile 35k15 35k65

Properties of positive solutions to a nonlinear parabolic problem

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Science China Mathematics 2007年第4期50卷 590-608页

作者： Hui-ling LI Ming-xin WANG Department of Mathematics Southeast UniversityNanjing 210018China

This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vázquez and the comparison principle, we deduce that the blow-up occurs only on the boundary ?Ω. In addition, for a bounded Lipschitz domain Ω, we establish the blow-up rate estimates for the positive solution to this problem with a = 0.

关键词： quasilinear parabolic equation blow-up global existence blow-up rate blow-up set 35k60 35B40 35k65

A NOTE ON THE BEHAVIOR OF BLOW-UP SOLUTIONS FOR ONE-PHASE STEFAN PROBLEMS

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Applied Mathematics(A Journal of Chinese Universities) 1998年第3期13卷 241-250页

作者： ZHUNING DepartmentofMathematics SuzhouUniversitySuzhou215006.

In this paper, the following one-phase Stefan problem is considered: u1=uxx+f（u，t）in Q1(T)，u（x,0）=u（x），0≤x≤t0，δu/δx（0,t）=0，0＜t≤T，u（l(t),t）=0，0＜t≤T，l'（t）=-ux（l(t),t），l（0）=l0，where Q1(T)={(x,t)|0＜x＜l(t)，0＜t≤T）and l0＞*** is proved that when the solution is blow-up in a finite time s(uo)+ and u0(x) is not a constant, then the free boundary will not be blow-up and the blow-up set is contained in the interval [0,l0). Moreover, when f(u,t)=u^1+μ for some μ>0, every blow-up point is isolated.

关键词： 35k65 35D05 One-Phase Stefan problem blow-up solution