On the maximal regularity for a class of Volterra integro-differential equations

A. Amansag, H. Bounit, A. Driouich, S. Hadd

备注：: 17 pages

英文摘要：

We propose an approach based on perturbation theory to establish maximal $L^p$-regularity for a class of integro-differential equations. As the left shift semigroup is involved for such equations, we study maximal regularity on Bergman spaces for autonomous and non-autonomous integro-differential equations. Our method is based on the formulation of the integro-differential equations to a Cauchy problems, infinite dimensional systems theory and some recent results on the perturbation of maximal regularity (see \cite{AmBoDrHa}). Applications to heat equations driven by the Dirichlet (or Neumann)-Laplacian are considered.

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