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2002 On a class of doubly nonlinear nonlocal evolution equations
Ulisse Stefanelli
Differential Integral Equations 15(8): 897-922 (2002).

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.

Citation

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Ulisse Stefanelli. "On a class of doubly nonlinear nonlocal evolution equations." Differential Integral Equations 15 (8) 897 - 922, 2002.

Information

Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1014.35051
MathSciNet: MR1895572

Subjects:
Primary: 34G25
Secondary: 35K55, 35K90, 45N05, 47H05, 47N20

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.15 • No. 8 • 2002
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