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Ying Zeng, Yanbo Hu, Global solutions to nonlinear wave equations arising from a variational principle

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DOI: 10.23952/jnva.8.2024.1.01

Volume 8, Issue 1, 1 February 2024, Pages 1-21

 

Abstract. In this paper, we establish the global existence of weak solutions to the initial-boundary value and initial value problems for two classes of nonlinear wave equations which are the Euler-Lagrange equation of a variational principle. We use the method of energy-dependent coordinates to rewrite these equations as semilinear systems and resolve all singularities by introducing a new set of dependent and independent variables. The global weak solutions can be constructed by expressing the solutions of these semilinear systems in terms of the original variables.

 

How to Cite this Article:
Y. Zeng, Y. Hu, Global solutions to nonlinear wave equations arising from a variational principle, J. Nonlinear Var. Anal. 8 (2024), 1-21.