Displaying similar documents to “Global existence for a semilinear prabolic Volterra equation.”

Second order semilinear Volterra integrodifferential equation in Banach space

Jan Bochenek (1992)

Annales Polonici Mathematici

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By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of some semilinear second order Volterra integrodifferential equations in Banach spaces is proved. The results are applied to some integro-partial differential equations.

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

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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.