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Abstract nonlinear Volterra integrodifferential equations with nonsmooth kernels

Maurizio Grasselli, Alfredo Lorenzi (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A Cauchy problem for an abstract nonlinear Volterra integrodifferential equation is considered. Existence and uniqueness results are shown for any given time interval under weak time regularity assumptions on the kernel. Some applications to the heat flow with memory are presented.

An algebraic derivative associated to the operator D δ

V. Almeida, N. Castro, J. Rodríguez (2000)

Banach Center Publications

In this paper we get an algebraic derivative relative to the convolution ( f * g ) ( t ) = 0 t i f ( t - ψ ) g ( ψ ) d ψ associated to the operator D δ , which is used, together with the corresponding operational calculus, to solve an integral-differential equation. Moreover we show a certain convolution property for the solution of that equation

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