Differential and Integral Equations

On a class of doubly nonlinear nonlocal evolution equations

Ulisse Stefanelli

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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

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

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34G25: Evolution inclusions
Secondary: 35K55: Nonlinear parabolic equations 35K90: Abstract parabolic equations 45N05: Abstract integral equations, integral equations in abstract spaces 47H05: Monotone operators and generalizations 47N20: Applications to differential and integral equations


Stefanelli, Ulisse. On a class of doubly nonlinear nonlocal evolution equations. Differential Integral Equations 15 (2002), no. 8, 897--922. https://projecteuclid.org/euclid.die/1356060778

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