LONG-TIME BEHAVIOR OF SOLUTIONS TO A CLASS OF FORWARD-BACKWARD PARABOLIC EQUATIONS

被引：14
|
作者：
Smarrazzo, Flavia [1 ]
Tesei, Alberto [1 ]
机构：
[1] Univ Roma La Sapienza, Dept Math G Castelnouvo, I-00185 Rome, Italy
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2010年 / 42卷 / 03期
关键词：
forward-backward parabolic equations; regularization; Young measures; entropy inequalities; long-time behavior of solutions; steady states; CAHN-HILLIARD EQUATIONS; DIFFUSION EQUATION; HEAT-EQUATION; LIMIT; REGULARIZATION; PARAMETER; EXISTENCE; DIRECTION; MODEL; FLOW;
D O I：
10.1137/090763561
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider weak entropy measure-valued solutions of the Neumann initial-boundary value problem for the equation u(t) = [phi(u)](xx), where phi is nonmonotone. These solutions are obtained from the corresponding problem for the regularized equation u(t) = [phi(u)](xx) vertical bar epsilon u(xxt) (epsilon > 0) by a vanishing viscosity method and satisfy a family of suitable entropy inequalities. Relying on a strong version of these inequalities, we prove exhaustive results concerning the long-time behavior of solutions.
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页码：1046 / 1093
页数：48
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