Initial–boundary value problems for nonlinear elliptic–parabolic equations with variable exponents of nonlinearity in unbounded domains without conditions at infinity. (March 2020)

• Record Type: Journal Article
• Authors: Bokalo, Mykola; Buhrii, Oleh; Hryadil, Nikolyetta
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: 35K65 -- 35K55 -- 35K70 -- 35D05; Elliptic–parabolic equation -- Variable exponent of nonlinearity -- Lebesgue and Sobolev spaces with variable exponents -- Unbounded domain; 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.2019.111700
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The paper is devoted to results of the investigation of the initial–boundary value problems for the nonlinear second order elliptic–parabolic equations with variable exponents of the nonlinearity in unbounded domains. We consider weak solutions which belong to the Lebesgue and Sobolev spaces with variable exponents. Under certain conditions on data-in the existence and uniqueness of the weak solutions are proved without conditions at infinity. Also some estimates of the weak solutions are obtained.