Gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces. (October 2019)

• Record Type: Journal Article
• Authors: Yang, Fei; Zhang, Liangdi
• Is Part Of: Nonlinear analysis. Volume 187(2019)
• Page Start: 49
• Page End: 70
• Publication Date: 2019-10
• Subjects: 35B45 -- 35K55 -- 53C21; Gradient estimates -- Harnack inequality -- Nonlinear parabolic equation -- Smooth metric measure space; 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.2019.03.017
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let ( M n, g, e − ϕ d v ) be a smooth metric measure space. In this paper, we derive a series of gradient estimates and a Harnack inequality for positive solutions of a nonlinear parabolic partial differential equation ( Δ ϕ − ∂ t ) u = q u + a u ( ln u ) α in M n × ( − ∞, + ∞ ), where q ∈ C 2, 1 ( M n × ( − ∞, + ∞ ) ) and a, α ∈ R .