Asymptotic analysis of a doubly nonlinear diffusion equation

King, John R.

Abstract

investigate the doubly nonlinear diffusion equation
∂u/∂t=1/n ∇.(u^m│∇u│^n-1) ∇u) and the same equation expressed in terms of a `pressure' variable. We classify various classes of compacted supported solutions, as well as finite-mass solutions that decay algebraically at infinity. A number of novel phenomena are identified, particularly for n<0, that seem to us worthy of further mathematical investigation.

Citation

King, J. R. (2016). Asymptotic analysis of a doubly nonlinear diffusion equation. Nonlinear Analysis: Theory, Methods and Applications, 138, https://doi.org/10.1016/j.na.2015.12.003

• Journal Article Type: Article
• Acceptance Date: Dec 2, 2015
• Online Publication Date: Dec 28, 2015
• Publication Date: Jun 1, 2016
• Deposit Date: Jun 23, 2016
• Publicly Available Date: Jun 23, 2016
• Journal: Nonlinear Analysis: Theory, Methods & Applications
• Electronic ISSN: 0362-546X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 138
• DOI: https://doi.org/10.1016/j.na.2015.12.003
• Keywords: Nonlinear diffusion; asymptotic analysis; moving boundary problems; image analysis
• Public URL: https://nottingham-repository.worktribe.com/output/787130
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0362546X15004125
• Contract Date: Jun 23, 2016