Finite time extinction in nonlinear diffusion equations

Peplow, A. T.; Beardmore, R. E.; Laister, R.

Abstract

We consider a class of degenerate diffusion equations where the nonlinearity is assumed to be singular (non-Lipschitz) at zero. It is shown that solutions with compactly supported initial data become identically zero in finite time. Such extinction follows by comparison with newly constructed finite travelling waves connecting two stable equilibria. © 2004 Elsevier Ltd. All rights reserved.

Citation

Beardmore, R. E., Peplow, A. T., & Laister, R. (2004). Finite time extinction in nonlinear diffusion equations. Applied Mathematics Letters, 17(5), 561-567. https://doi.org/10.1016/S0893-9659%2804%2990126-7

• Journal Article Type: Article
• Publication Date: Jan 1, 2004
• Journal: Applied Mathematics Letters
• Print ISSN: 0893-9659
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 17
• Issue: 5
• Pages: 561-567
• DOI: https://doi.org/10.1016/S0893-9659%2804%2990126-7
• Keywords: finite travelling waves, degenerate diffusion, singular, extinction
• Public URL: https://uwe-repository.worktribe.com/output/1060669
• Publisher URL: http://dx.doi.org/10.1016/S0893-9659(04)90126-7