Abstract
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.
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