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- W1595520009 abstract "The work is concerned with the existence and the qualitative behavior of solutions of certain nonlinear Volterra integro-differential equations. Both abstract equations with accretive operators and concrete equations of elliptic-parabolic type are considered. Equations of this type arise in the theory of heat ow in materials with memory and diffusion of uids in porous media with memory. Existence and uniqueness of entropy solutions is obtained for a concretehistory dependent elliptic-parabolic initial boundary value problem for gen-eral integrable data. Regularity properties of solutions are considered. In particular, existence of strong solutions is shown if the state space is a Banach space without the Radon-Nikodym property. The asymptotic behavior of solutions is investigated. Conditions on thedata are obtained such that the solution is asymptotically almost periodic or weakly almost periodic in the sense of Eberlein. Keywords and phrases: entropy solutions, renormalized solutions, m-completely accretive operators, almost periodicity. AMS Subject Classification: 35B15, 35K65, 45K05, 45M05, 45N05, 47H06." @default.
- W1595520009 created "2016-06-24" @default.
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- W1595520009 date "2002-04-24" @default.
- W1595520009 modified "2023-10-16" @default.
- W1595520009 title "Nonlinear elliptic-parabolic integro-differential equations with L 1-data: existence, uniqueness, asymptotic" @default.
- W1595520009 hasPublicationYear "2002" @default.
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