Istituto di Matematica Applicata e Tecnologie Informatiche     
Stefanelli U. On Some Nonlocal Evolution Equations in Banach Spaces. Preprint ercim.cnr.ian//2001-1245, 2001.
This note is concerned with the initial value problem for the abstract nonlocal equation $, (Au)' + (Bu) ni f ,$ where $, A ,$ is a maximal monotone operator from a reflexive Banach space $, E ,$ to its dual $, E^* $, while $, B ,$ is a nonlocal maximal monotone operator from $, L^p(0,T;E) ,$ to $, L^q(0,T;E^*) ,$ with $, p^{-1} + q^{-1}=1$, $, p in (1,infty)$. Under proper boundedness and coercivity assumptions on the operators, a solution is achieved by means of a discretization argument. Uniqueness and continuous dependence are also discussed and we prove some estimates for the discretization error. Finally, we give some detail of the approximation of linear Volterra integrodifferential operators.
Subject Doubly nonlinear evolution equations, nonlocal term, Volterra operators
35K90, 45N05

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