Existence of solutions for some doubly degenerate parabolic equations with natural growth terms. (September 2015)

• Record Type: Journal Article
• Authors: Zou, Weilin; Wang, Wei
• Is Part Of: Nonlinear analysis. Volume 125(2015)
• Page Start: 150
• Page End: 166
• Publication Date: 2015-09
• Subjects: 35J87 -- 47J20 -- 35A01 -- 35A02; Existence -- Degenerate parabolic equations -- Natural growth -- L∞ estimate; 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.2015.05.007
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper deals with a class of doubly degenerate parabolic equations of the type ∂ b ( u ) ∂ t − div ( a ( x, t, u, ∇ u ) ) + F ( x, t, u, ∇ u ) = f, where b is a strictly increasing C 1 -function. Under some suitable hypothesis, we prove that there exists at least a bounded solution to this problem in standard weak sense.