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Implicit Degenerate Evolution Equations and Applications

Description: 
The initial-value problem is studied for evolution equations in Hilbert space of the general form d/dt A(u) + B(u) ϶ f, where and are maximal monotone operators. Existence of a solution is proved when A is a subgradient and either is strongly monotone or B is coercive; existence is established also in the case where A is strongly monotone and B is subgradient. Uniqueness is proved when one of A or B is continuous self-adjoint and the sum is strictly monotone; examples of nonuniqueness are given. Applications are indicated for various classes of degenerate nonlinear partial differential equations or systems of mixed elliptic-parabolic-pseudoparabolic types and problems with nonlocal nonlinearity.
Publisher: 
Society for Industrial and Applied Mathematics
Type: 
Article
Raw Url: 
http://ir.library.oregonstate.edu?metadataPrefix=&verb=GetRecord&identifier=ir.library.oregonstate.edu:xp68kg80s
Repository Record Id: 
ir.library.oregonstate.edu:xp68kg80s
Contributor: 
Mathematics
Record Title: 
Implicit Degenerate Evolution Equations and Applications
Identifier: 
http://ir.library.oregonstate.edu/concern/articles/xp68kg80s
Author: 
Di Benedetto, Emmanuele
Showalter, R. E.
Database: 
Resource OE Format: 
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