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2008 A free boundary characterization of measure-valued solutions for forward-backward diffusion
Dirk Horstmann, Ben Schweizer
Adv. Differential Equations 13(3-4): 201-227 (2008).

Abstract

We consider a nonlinear one-dimensional scalar equation of diffusion type in which, depending on the gradient of the solution, the diffusion coefficient may be positive or negative. We compare two concepts of Young measure solutions which are based on different methods to construct approximate solutions, the SP-solutions (singular perturbation) and the EM-solution (energy minimization). We show that the SP-solution can recover classical solutions where the EM-solution fails to do so, and that EM-solutions are more stable under perturbations of the initial values. We characterize the EM-solution with a free boundary problem and determine its long-time behavior.

Citation

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Dirk Horstmann. Ben Schweizer. "A free boundary characterization of measure-valued solutions for forward-backward diffusion." Adv. Differential Equations 13 (3-4) 201 - 227, 2008.

Information

Published: 2008
First available in Project Euclid: 18 December 2012

zbMATH: 1180.35306
MathSciNet: MR2482417

Subjects:
Primary: 35K57
Secondary: 35B40, 35K65, 35R35

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.13 • No. 3-4 • 2008
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