Advances in Differential Equations

A free boundary characterization of measure-valued solutions for forward-backward diffusion

Dirk Horstmann and Ben Schweizer

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Adv. Differential Equations Volume 13, Number 3-4 (2008), 201-227.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867349

Mathematical Reviews number (MathSciNet)
MR2482417

Zentralblatt MATH identifier
1180.35306

Subjects
Primary: 35K57: Reaction-diffusion equations
Secondary: 35B40: Asymptotic behavior of solutions 35K65: Degenerate parabolic equations 35R35: Free boundary problems

Citation

Horstmann, Dirk; Schweizer, Ben. A free boundary characterization of measure-valued solutions for forward-backward diffusion. Adv. Differential Equations 13 (2008), no. 3-4, 201--227. https://projecteuclid.org/euclid.ade/1355867349.


Export citation