Cauchy problem for doubly degenerate parabolic equation with gradient source. (January 2015)

• Record Type: Journal Article
• Authors: Shang, Haifeng; Cheng, Junxiang
• Is Part Of: Nonlinear analysis. Volume 113(2015)
• Page Start: 323
• Page End: 338
• Publication Date: 2015-01
• Subjects: 35K15 -- 35K55 -- 35K65; Doubly nonlinear parabolic equation -- Cauchy problem -- Gradient source -- Local existence; 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.2014.10.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider the Cauchy problem for a doubly degenerate parabolic equation with a source term depending solely on the gradient. A major result of this paper is to establish the local existence of solutions for this equation under optimal stipulated assumptions on the initial data.