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Lingfang Xu, Gan Yin, Yanbo Hu, Conservative solutions to the first initial-boundary value problem for a nonlinear variational wave equation

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DOI: 10.23952/jnva.9.2025.2.06

Volume 9, Issue 2, 1 April 2025, Pages 263-282

 

Abstract. This paper concerns with the first initial-boundary value problem for a one-dimensional nonlinear variational wave equation which is the Euler-Lagrange equation of a variational principle. We introduce the energy-dependent coordinates into the finite interval to transform the original problem into a boundary value problem of a semilinear system. The global existence of weak solutions for the new boundary value problem is first established by deriving the a priori estimates and then expressed in terms of the original variables.

 

How to Cite this Article:
L. Xu, G. Yin, Y. Hu, Conservative solutions to the first initial-boundary value problem for a nonlinear variational wave equation, J. Nonlinear Var. Anal. 9 (2025), 263-282.