Istituto di Matematica Applicata e Tecnologie Informatiche     
Aizicovici S., Colli P., Grasselli M. Doubly nonlinear evolution equations with memory. Preprint ercim.cnr.ian//1999-1125, 1999.
A nonlinear abstract integrodifferential evolution equation of Volterra type is considered. This equation contains two main nonlinearities, expressed by a maximal monotone operator and a subdifferential of a suitable convex and lower semicontinuous function, respectively. By means of a semi-implicit time discretization procedure, the existence of solutions to the Cauchy problem associated with the evolution equation is proved. Then, the abstract result is applied to initial and boundary value problems for a nonlinear system with memory subject to nonlinear boundary conditions, and for a Stefan problem with a nonlinear heat flux law with memory.
Subject 34G20, 45K05, 47G20, 80A22

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