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
Show me the PDF file (314 KB), TEX file for this article.
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 |
Return to the EJDE web page