A comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups. (February 2022)

• Record Type: Journal Article
• Authors: Ruzhansky, Michael; Yessirkegenov, Nurgissa
• Is Part Of: Nonlinear analysis. Volume 215(2022)
• Publication Date: 2022-02
• Subjects: 35G20 -- 22E30; Nonlinear hypoelliptic heat equation -- Rockland operator -- p-sub-Laplacian -- Comparison principle -- Graded Lie group -- Stratified Lie group -- Global solution -- Blow-up; 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.2021.112621
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we present a comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups. Moreover, using the comparison principle we obtain blow-up type results and global in t -boundedness of solutions of nonlinear equations for the heat p -sub-Laplacian on stratified Lie groups.