Stefanelli U. On a class of doubly nonlinear nonlocal evolution equations. Preprint ercim.cnr.ian//2001-1252, 2001. |

Abstract (English) |
This note deals with the initial value problem for the abstract nonlinear nonlocal equation $ (A u)' + (B u) ni f $, where $ A $ is a possibly degenerate maximal monotone operator from the Hilbert space $ V $ to its dual space $ V ^* $, while $ 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 $ 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. | |

Subject | Nonlocal evolution equations, approximation 35K55, 45N05 |

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