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Article Dans Une Revue Dynamics of Continuous, Discrete and Impulsive Systems, Serie A Année : 2009

Pseudo almost automorphic solutions for hyperbolic semilinear evolution equations in intermediate Banach spaces

Résumé

We are concerned in this paper with the pseudo almost automorphy of mild solutions for the semilinear evolution equation $x'(t)=Ax(t)+f(t,x)$ where $A$ is a sectorial operator not necessarily densely defined in $X$ generating an hyperbolic semigroup $(T(t))_{t\geq 0}$ in a Banach space $X$ and $f:\R\times X_\alpha \to X$, where $X_{\alpha}$ is an intermediate space. We prove the existence and uniqueness of a pseudo almost automorphic solution in $X_\alpha$, when the function $f:\R\times X_\alpha\longrightarrow X$ is pseudo almost automorphic.
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Dates et versions

hal-00617632 , version 1 (29-08-2011)

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  • HAL Id : hal-00617632 , version 1

Citer

Gaston N'Guérékata, Denis Pennequin. Pseudo almost automorphic solutions for hyperbolic semilinear evolution equations in intermediate Banach spaces. Dynamics of Continuous, Discrete and Impulsive Systems, Serie A, 2009, supp., pp.266-270. ⟨hal-00617632⟩
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