Dirichlet conditions at infinity for parabolic and elliptic equations. (June 2016)

• Record Type: Journal Article
• Authors: Kamin, Shoshana; Punzo, Fabio
• Is Part Of: Nonlinear analysis. Volume 138(2016)
• Page Start: 156
• Page End: 175
• Publication Date: 2016-06
• Subjects: 35J25 -- 35J70 -- 35K15 -- 35K55 -- 35K65; Parabolic equations -- Unbounded coefficients -- Conditions at infinity; 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.2015.11.001
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in R N × R + . Under specific assumptions, we establish existence of solutions satisfying prescribed conditions at infinity, depending on the direction along which infinity is approached. Moreover, the large-time behavior of such solutions is addressed. We consider also elliptic equations in R N with similar conditions at infinity.