Global solutions to a one-dimensional nonlinear wave equation derivable from a variational principle

Date
2017-11-28
Authors
Hu, Yanbo
Wang, Guodong
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This article focuses on a one-dimensional nonlinear wave equation which is the Euler-Lagrange equation of a variational principle whose Lagrangian density involves linear terms and zero term as well as quadratic terms in derivatives of the field. We establish the global existence of weak solutions to its Cauchy problem by the method of energy-dependent coordinates which allows us to rewrite the equation as a semilinear system and resolve all singularities by introducing a new set of variables related to the energy.
Description
Keywords
Nonlinear wave equation, Weak solutions, Existence, Energy-dependent coordinates
Citation
Hu, Y., & Wang, G. (2017). Global solutions to a one-dimensional nonlinear wave equation derivable from a variational principle. <i>Electronic Journal of Differential Equations, 2017</i>(294), pp. 1-20.