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Time compactness tools for discretized evolution equations and applications to degenerate parabolic PDEs

Abstract : We discuss several techniques for proving compactness of sequences of approximate solutions to discretized evolution PDEs. While the well-known Aubin-Simon kind functional-analytic techniques were recently generalized to the discrete setting by Gallouët and Latché [15], here we discuss direct techniques for estimating the time translates of approximate solutions in the space $L^1$. One important result is the Kruzhkov time compactness lemma. Further, we describe a specific technique that relies upon the order-preservation property. Motivation comes from studying convergence of finite volume discretizations for various classes of nonlinear degenerate parabolic equations. These and other applications are briefly described.
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Contributor : Boris Andreianov <>
Submitted on : Thursday, February 24, 2011 - 2:03:49 PM
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Boris Andreianov. Time compactness tools for discretized evolution equations and applications to degenerate parabolic PDEs. Finite Volumes for Complex Applications VI, Jun 2011, Prague, Czech Republic. pp. 21-29, ⟨10.1007/978-3-642-20671-9_3⟩. ⟨hal-00561344v2⟩

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