Propagation and extinction of fronts for semilinear parabolic equations on Riemannian manifolds. (January 2016)

• Record Type: Journal Article
• Authors: Punzo, Fabio
• Is Part Of: Nonlinear analysis. Volume 131(2016)
• Page Start: 325
• Page End: 345
• Publication Date: 2016-01
• Subjects: 35J25 -- 35J70 -- 35K15 -- 35K55 -- 35K65; Semilinear parabolic equations -- Propagation and extinction of fronts -- Riemannian manifolds; 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.2015.09.010
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the Cauchy problem for the semilinear heat equation on Riemannian manifolds. Propagation and extinction of solutions are addressed, supposing that the nonlinear forcing term is either of KPP type or of bistable type. In particular, we highlight the influence both of sectional curvatures and of Ricci curvature on such phenomena.