On the Cauchy problem for a nonlinear variational wave equation with degenerate initial data. (November 2018)

• Record Type: Journal Article
• Authors: Hu, Yanbo; Wang, Guodong
• Is Part Of: Nonlinear analysis. Volume 176(2018)
• Page Start: 192
• Page End: 208
• Publication Date: 2018-11
• Subjects: 35L20 -- 35L70 -- 35L80; Variational wave equation -- Degenerate hyperbolic -- Cauchy problem -- Weighted metric space; 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.2018.06.013
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is focused on a one-dimensional nonlinear variational wave equation which is the Euler–Lagrange equations of a variational principle arising in the theory of nematic liquid crystals and a few other physical contexts. We establish the local existence and uniqueness of classical solutions to its Cauchy problem with initial data given on the parabolic degenerating line.