Existence of peaking solutions for semilinear heat equations with blow-up profile above the singular steady state. (April 2019)

• Record Type: Journal Article
• Authors: Naito, Yūki; Senba, Takasi
• Is Part Of: Nonlinear analysis. Volume 181(2019)
• Page Start: 265
• Page End: 293
• Publication Date: 2019-04
• Subjects: 35K58 -- 35B44 -- 35C06 -- 35A24; Semilinear heat equation -- Incomplete blow-up -- Self-similar solution -- Peaking solution; 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.2018.12.001
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider positive solutions of the semilinear heat equation with supercritical power nonlinearity, and construct peaking solutions by connecting a backward self-similar solution with a forward self-similar solution. In particular, we show the existence of incomplete blow-up solutions with blow-up profile above the singular steady state. We also show the existence of a minimal continuation and obtain some properties of non-minimal continuations.