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Attractors in $L^2(\bbfR^N)$ for a class of reaction-diffusion equations. (English) Zbl 1221.35203
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 $L^2(\Bbb R^N)$. 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)].

##### MSC:
 35K57 Reaction-diffusion equations 35B41 Attractors (PDE) 47H20 Semigroups of nonlinear operators 34C20 Transformation and reduction of ODE and systems, normal forms 34D20 Stability of ODE
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##### References:
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