Convergence rate to singular steady states in a semilinear parabolic equation. (January 2016)

• Record Type: Journal Article
• Authors: Hoshino, Masaki; Yanagida, Eiji
• Is Part Of: Nonlinear analysis. Volume 131(2016)
• Page Start: 98
• Page End: 111
• Publication Date: 2016-01
• Subjects: primary 35K58 -- secondary 35B33 35B35; Semilinear parabolic equation -- Singular solution -- Steady state -- Convergence rate; 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.2015.06.020
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the asymptotic behavior of singular solutions of a semilinear parabolic equation. Our aim is to determine a convergence rate to singular steady states, and to derive a universal lower bound of the convergence rate which implies the optimality of the convergence rate. Proofs are given by using a super- and subsolution method based on matched asymptotic expansion.