Existence of smooth solutions to a one-dimensional nonlinear degenerate variational wave equation. (December 2017)

• Record Type: Journal Article
• Authors: Hu, Yanbo; Wang, Guodong
• Is Part Of: Nonlinear analysis. Volume 165(2017)
• Page Start: 80
• Page End: 101
• Publication Date: 2017-12
• Subjects: 35L20 -- 35L70 -- 35L80; Variational wave equation -- Degenerate hyperbolic -- Characteristic decomposition -- Bootstrap; 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.2017.09.009
• 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 global existence of smooth solutions to its degenerate initial–boundary value problem under relaxed conditions on the initial–boundary data. Moreover, we show that the solution is uniformly C 1, α continuous up to the degenerate boundary and the degenerate curve is C 1, α continuous for α ∈ ( 0, 1 2 ) .