Asymptotic analysis of a doubly nonlinear diffusion equation. (June 2016)

• Record Type: Journal Article
• Authors: King, J.R.
• Is Part Of: Nonlinear analysis. Volume 138(2016)
• Page Start: 253
• Page End: 276
• Publication Date: 2016-06
• Subjects: Nonlinear diffusion -- Moving boundary problems -- Image analysis; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.12.003
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We 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.