Jin Zhang, Chang Zhang, Chengkui Zhong
Abstract:
We consider the existence of global attractor for the inhomogeneous
reaction-diffusion equation
where
is supercritical and V(x) satisfies suitable
assumptions. Since
is not positive definite in
,
the Gronwall inequality can not be derived and the corresponding semigroup
does not possess bounded absorbing sets in
.
Thus,
by a special method, we prove that the equation has a global attractor
in
,
which attracts any bounded subset in
.
Submitted July 20, 2015. Published March 4, 2016.
Math Subject Classifications: 35B41, 35K57, 37L99.
Key Words: Global attractor; inhomogeneous reaction-diffusion equation;
unbounded domain; supercritical nonlinearity.
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Jin Zhang Department of Mathematics, College of Science Hohai University Nanjing 210098, China email: zhangjin86@hhu.edu.cn | |
Chang Zhang Department of Mathematics, Nanjing University Nanjing 210093, China email: chzhnju@126.com | |
Chengkui Zhong Department of Mathematics, Nanjing University Nanjing 210093, China email: ckzhong@nju.edu.cn |
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