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Zbl 1221.35203
Zhang, Yanhong; Zhong, Chengkui; Wang, Suyun
(Zhang, Yan-hong; Zhong, Cheng-kui; Wang, Su-yun)
Attractors in $L^2(\bbfR^N)$ for a class of reaction-diffusion equations. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 5-6, A, 1901-1908 (2009). ISSN 0362-546X

The authors study the class of nonlinear reaction-diffusion equations: $$ \align &\frac{\partial u}{\partial t} = b\Delta u - cu - f(u) - a(x)h(u) + g(x), \quad x \in \Bbb R^N,\\ &u(x,0) = u_0(x). \endalign $$ They prove the existence of a global attractor $A$ in $L^2(\Bbb R^N)$ for the semigroup associated to this problem; $A$ is compact, invariant and attracts every bounded subsets of $L^2(\Bbb R^N)$. \par The proof relies on results of {\it Q.-F. Ma, S.-H. Wang} and {\it C.-K. Zhong} [Indiana Univ.\ Math. J. 51, No.,6, 1542--1558 (2002; Zbl 1028.37047)].
[Marlène Frigon (Montréal)]

MSC 2000:: *35K57 Reaction-diffusion equations
35B41 Attractors
47H20 Semigroups of nonlinear operators
34C20 Transformation of ODE and systems
34D20 Lyapunov stability of ODE

Keywords: nonlinear reaction-diffusion equation; $\omega$-limit compactness; absorbing set; global attractor

Citations: Zbl 1028.37047

Cited in: Zbl 1191.35070

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