Existence of solutions to nonlinear parabolic equations via majorant integral kernel. (October 2022)

• Record Type: Journal Article
• Authors: Ishige, Kazuhiro; Kawakami, Tatsuki; Okabe, Shinya
• Is Part Of: Nonlinear analysis. Volume 223(2022)
• Publication Date: 2022-10
• Subjects: Fractional semilinear parabolic equations -- Higher-order semilinear parabolic equations -- Majorant integral kernel -- Existence of solutions, integral equation; 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.2022.113025
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We establish the existence of solutions to the Cauchy problem for a large class of nonlinear parabolic equations including fractional semilinear parabolic equations, higher-order semilinear parabolic equations, and viscous Hamilton–Jacobi equations by using the majorant kernel introduced in Ishige et al. (2020).