Existence of solutions of degenerate parabolic equations with inhomogeneous density and growing data on manifolds. (June 2022)

• Record Type: Journal Article
• Authors: Andreucci, Daniele; Tedeev, Anatoli F.
• Is Part Of: Nonlinear analysis. Volume 219(2022)
• Publication Date: 2022-06
• Subjects: 35K55 -- 35K65 -- 35B40; Doubly degenerate parabolic equation -- Noncompact Riemannian manifold -- Inhomogeneous density -- Optimal growth; 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.2022.112818
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider doubly non-linear degenerate parabolic equations on Riemannian manifolds of infinite volume. The equation is inhomogeneous: indeed it contains a capacitary coefficient depending on the space variable, which we assume to decay at infinity. We prove existence of solutions for initial data growing at infinity in a suitable admissible class and some related estimates. We also prove, independently, a sup bound valid in the same geometrical setting for solutions which are a priori known to have compact support; the majorization depends on the size of the support.