Electron. J. Differential Equations, Vol. 2017 (2017), No. 294, pp. 1-20.

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

Yanbo Hu, Guodong Wang

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.

Submitted October 13, 2017. Published November 28, 2017.
Math Subject Classifications: 35D05, 35L15, 35L70.
Key Words: Nonlinear wave equation; weak solutions; existence; energy-dependent coordinates

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Yanbo Hu
Department of Mathematics
Hangzhou Normal University
Hangzhou, 310036, China
email: yanbo.hu@hotmail.com
Guodong Wang
School of Mathematics & Physics
Anhui Jianzhu University
Hefei, 230601, China
email: yxgdwang@163.com

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