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Article Dans Une Revue Cubo, a Mathematical Journal Année : 2008

Existence and Uniqueness of Pseudo Almost Automorphic Solutions to Some Classes of Partial Evolution Equations

Résumé

In this paper, we study pseudo almost automorphic solutions to perturbations to Eq.\;(\ref{1}) consisting of the class of abstract partial evolution equations of the form \begin{eqnarray}\label{2} \displaystyle{\frac{d}{dt}} \left[u(t) + f(t, u(t))\right] = A u(t) \; \; t \in \R, \end{eqnarray} where $A$ is the infinitesimal generator of an exponentially stable $c_0$-semigroup acting on $\X$, $B, C$ are two densely defined closed linear operators on $\X$, and $f$ is continuous functions. Under some appropriate assumptions, we establish the existence and uniqueness of an almost automorphic (mild) solution to Eq.\,(\ref{2}) using the Banach fixed-point principle.
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Dates et versions

hal-00617633 , version 1 (29-08-2011)

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  • HAL Id : hal-00617633 , version 1

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Gaston N'Guérékata, Denis Pennequin. Existence and Uniqueness of Pseudo Almost Automorphic Solutions to Some Classes of Partial Evolution Equations. Cubo, a Mathematical Journal, 2008, 10 (3), pp.161-170. ⟨hal-00617633⟩
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