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1996 On mild and weak solutions of elliptic-parabolic problems
Philippe Benilan, Petra Wittbold
Adv. Differential Equations 1(6): 1053-1073 (1996).

Abstract

We consider an elliptic-parabolic equation in divergence form $b(v)_t = \text{div}\alpha(v, Dv)+ f$ with Dirichlet boundary conditions and initial condition. Under rather general assumptions, we prove existence of mild solutions satisfying an $L^1$-comparison principle; under some additional conditions, these solutions are shown to be weak solutions. Moreover, under the general assumptions, uniqueness of integral solutions is established; under certain conditions, we show that weak solutions are integral solutions. The notions of mild and integral solutions are derived from nonlinear semigroup theory; by this approach, we extend and make precise former results on existence and uniqueness of weak solutions.

Citation

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Philippe Benilan. Petra Wittbold. "On mild and weak solutions of elliptic-parabolic problems." Adv. Differential Equations 1 (6) 1053 - 1073, 1996.

Information

Published: 1996
First available in Project Euclid: 25 April 2013

zbMATH: 0858.35064
MathSciNet: MR1409899

Subjects:
Primary: 35M10
Secondary: 35D05 , 35K60

Rights: Copyright © 1996 Khayyam Publishing, Inc.

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Vol.1 • No. 6 • 1996
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