Nonexistence results for a semilinear heat equation with bounded potentials. (March 2020)

• Record Type: Journal Article
• Authors: Phan, Quoc Hung
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: primary 35B53 35K55 -- secondary 35B33; Liouville-type theorem -- Parabolic equation -- Critical exponent; 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.2019.111667
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the Liouville type theorem for positive solutions to the semilinear heat equation u t − Δ u = V u p in R N × R . We show that the nonexistence of positive solutions holds for any p < 1 and for any V bounded from below by a positive constant. In the superlinear case p > 1, we give some sufficient conditions on the potential and the exponent which guarantee the nonexistence of positive solutions in the whole space.