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Fan, Zhao-hui

Exponential attractors for parabolic equations with dynamic boundary conditions. (English) Zbl 1266.35115

J. Appl. Math. 2013, Article ID 389863, 6 p. (2013).
Summary: We study exponential attractors for semilinear parabolic equations with dynamic boundary conditions in bounded domains. First, we give the existence of the exponential attractor in \(L^2(\Omega) \times L^2(\Gamma)\) by proving that the corresponding semigroup satisfies the enhanced flattering property. Second, we apply asymptotic a priori estimate and obtain the exponential attractor in \(L^p(\Omega) \times L^q(\Gamma)\). Finally, we show the exponential attractor in \((H^1(\Omega) \cap L^p(\Omega)) \times L^q(\Gamma)\).

MSC:

35K58 Semilinear parabolic equations
35B41 Attractors
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\textit{Z.-h. Fan}, J. Appl. Math. 2013, Article ID 389863, 6 p. (2013; Zbl 1266.35115)
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