## Differential and Integral Equations

### On a class of doubly nonlinear nonlocal evolution equations

Ulisse Stefanelli

#### Abstract

This note deals with the initial value problem for the abstract nonlinear nonlocal equation $(\mathcal A u)' + (\mathcal B u) \ni f$, where $\mathcal A$ is a possibly degenerate maximal monotone operator from the Hilbert space $V$ to its dual space $V ^*$, while $\mathcal B$ is a nonlocal maximal monotone operator from $L^2(0,T,V)$ to $L^2(0,T;V^*)$. Assuming suitable boundedness and coerciveness conditions and letting $\mathcal A$ be a subgradient, existence of a solution is established by making use of an approximation procedure. Applications to various classes of degenerate nonlinear integrodifferential equations are discussed.

#### Article information

Source
Differential Integral Equations, Volume 15, Number 8 (2002), 897-922.

Dates
First available in Project Euclid: 21 December 2012