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SOME RESULTS ON A DEGENERATE AND SINGULAR DIFFUSION EQUATION 被引量:1
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作者 姚正安 周文书 《Acta Mathematica Scientia》 SCIE CSCD 2007年第3期581-601,共21页
In this article, a degenerate and singular diffusion problem is studied. The existence of solutions is established by parabolic regularization. Some properties of solutions, for instance, asymptotic behavior, are also... In this article, a degenerate and singular diffusion problem is studied. The existence of solutions is established by parabolic regularization. Some properties of solutions, for instance, asymptotic behavior, are also discussed. 展开更多
关键词 degenerate and singular diffusion equation weak solution EXISTENCE asymptotic behavior
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THE BLOW-UP PROPERTIES FOR A DEGENERATE SEMILINEAR PARABOL IC EQUATION WITH NONL OCAL SOURCE 被引量:5
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作者 Chen Youpeng Liu Qilin Xie ChunhongDept. of Math., Nanjing Univ.,Nanjing 210093,China. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2002年第4期413-424,共12页
This paper deals with the blow up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equation u t-(x αu x) x=∫ a 0f(u) d x in (0,a)×(0,T) under homogeneous Dirichl... This paper deals with the blow up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equation u t-(x αu x) x=∫ a 0f(u) d x in (0,a)×(0,T) under homogeneous Dirichlet conditions. The local existence and uniqueness of classical solution are established. Under appropriate hypotheses, the global existence and blow up in finite time of positive solutions are obtained. It is also proved that the blow up set is almost the whole domain. This differs from the local case. Furthermore, the blow up rate is precisely determined for the special case: f(u)=u p,p>1. 展开更多
关键词 degenerate and singular parabolic equation nonlocal reaction global existence finite time blow up asymptotic behavior of solution.
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GLOBAL BLOW-UP FOR A LOCALIZED DEGENERATE AND SINGULAR PARABOLIC EQUATION WITH WEIGHTED NONLOCAL BOUNDARY CONDITIONS 被引量:1
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作者 Baozhu Zheng Youpeng Chen 《Annals of Differential Equations》 2014年第4期484-493,共10页
This paper deals with the blow-up properties of positive solutions to a localized degenerate and singular parabolic equation with weighted nonlocal boundary condi- tions. Under appropriate hypotheses, the global exist... This paper deals with the blow-up properties of positive solutions to a localized degenerate and singular parabolic equation with weighted nonlocal boundary condi- tions. Under appropriate hypotheses, the global existence and finite time blow-up of positive solutions are obtained. Furthermore, the global blow-up behavior and the uniform blow-up profile of blow-up solutions are also described. We find that the blow-up set is the whole domain {0, a}, including the boundaries, and this differs from parabolic equations with local sources case or with homogeneous Dirichlet boundary conditions case. 展开更多
关键词 localized degenerate and singular parabolic equation weighted nonlo-cal boundary condition global existence finite time blow-up uniform blow-up profile
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GLOBAL BLOW-UP FOR A DEGENERATE AND SINGULAR NONLOCAL PARABOLIC EQUATION WITH WEIGHTED NONLOCAL BOUNDARY CONDITIONS
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作者 Xingying Liu Baozhu Zheng Youpeng Chen 《Annals of Applied Mathematics》 2015年第3期313-324,共12页
This paper deals with the blow-up properties of positive solutions to a degenerate and singular nonlocal parabolic equation with weighted nonlocal boundary conditions. Under appropriate hypotheses, the global existenc... This paper deals with the blow-up properties of positive solutions to a degenerate and singular nonlocal parabolic equation with weighted nonlocal boundary conditions. Under appropriate hypotheses, the global existence and finite time blow-up of positive solutions are obtained. Furthermore, by using the properties of Green's function, we find that the blow-up set of the blow-up solution is the whole domain (0, a), and this differs from parabolic equations with local sources case. 展开更多
关键词 degenerate and singular parabolic equation weighted nonlocal boun-dary condition global existence finite time blow-up Green's function
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Regularity of Solutions of Certain Parabolic System with Nonstandard Growth Condition
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作者 You Jiangsheng (Department of Mathematics and Institute of Heavy Ion Physics Peking University,Beijing 100871,China) 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1998年第2期145-160,共16页
By the use of Moser iteration and Campanato space estimate,the L~∞ and C~α regularity gradient of solutions of nonlinear parabolic system (u^2)/(t)-▽(g|▽u|▽u^2)=0 with nonstandard growth conditions are obtained u... By the use of Moser iteration and Campanato space estimate,the L~∞ and C~α regularity gradient of solutions of nonlinear parabolic system (u^2)/(t)-▽(g|▽u|▽u^2)=0 with nonstandard growth conditions are obtained under the natural structure constraints. 展开更多
关键词 Nonstandard growth condition degenerate and singular equations Moser iteration Campanato space estimate
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