Istituto di Matematica Applicata e Tecnologie Informatiche     
Stefanelli U. Well-posedness and Time Discretization of a Nonlinear Volterra Integrodifferential Equation. Preprint ercim.cnr.ian//1999-1168, 1999.
This paper deals with a nonlinear abstract evolution integrodifferential equation of Volterra type. This equation contains two nonlinearities, namely a maximal monotone operator and a Lipschitz continuous operator, and may arise from a Stefan problem in materials with memory. Uniqueness of a solution to the associated Cauchy problem is proved. Then, global existence is achieved via a semi-implicit time discretization procedure. Moreover, some estimates for the discretization error are established.
Subject Nonlinear Volterra integrodifferential equation, abstract Cauchy problem, time discretization, existence and uniqueness, convergence result, error estimate
80A22, 45K05, 45L10, 65M15

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