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THE FIRST BOUNDARY VALUE PROBLEM FOR STRONGLY DEGENERATE QUASILINEAR PARABOLIC EQUATIONS IN ANISOTROPIC SOBOLEV SPACES 被引量:1
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作者 招燕燕 陈祖墀 《Acta Mathematica Scientia》 SCIE CSCD 2006年第2期255-264,共10页
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... 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 anisotropic Sobolev spaces an existence result is proved. 展开更多
关键词 Weak solution strongly degenerate quasilinear parabolic equation 2000 MR Subject Classification 35K55 35K60 35k65
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GLOBAL SOLUTION OF NONLINEAR DEGENERATE SYSTEMS OF FILTRATION TYPE IN SEVERAL SPACE VARIABLES
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作者 Lu Guofu 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1999年第1期30-44,共15页
In this paper the following nonlinear degenerate parabolic systemsu t=Δ x( grad φ(u))+α·Δb(u)+f(x,t,u)with Dirichlet boundary conditions are discussed, where u, grad φ(u),b and f are vector value... In this paper the following nonlinear degenerate parabolic systemsu t=Δ x( grad φ(u))+α·Δb(u)+f(x,t,u)with Dirichlet boundary conditions are discussed, where u, grad φ(u),b and f are vector valued functions and x∈Ω R N. Under some structure conditions on the terms of the systems, the results on existence and uniqueness of global solutions of the systems are established. 展开更多
关键词 1991 MR Subject Classification 35k65 35R35
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Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries 被引量:11
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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 《Science China Mathematics》 SCIE 2007年第9期1251-1266,共16页
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 solu... 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. 展开更多
关键词 parabolic system nonlocal sources nonlocal boundary conditions blow-up set simultaneous blow-up uniform blow-up profile 35K15 35k65
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On the Cauchy problem for a doubly nonlinear degenerate parabolic equation with strongly nonlinear sources 被引量:1
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作者 ZHENG TingTing ZHAO JunNing 《Science China Mathematics》 SCIE 2008年第11期2059-2071,共13页
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 conditi... 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. 展开更多
关键词 degenerate parabolic nonlinear sources global and local solutions 35k65 35K55
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Properties of positive solutions to a nonlinear parabolic problem
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作者 Hui-ling LI Ming-xin WANG 《Science China Mathematics》 SCIE 2007年第4期590-608,共19页
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 so... 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. 展开更多
关键词 quasilinear parabolic equation BLOW-UP global existence blow-up rate blow-up set 35K60 35B40 35k65
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