Electron. J. Differential Equations,
Vol. 2017 (2017), No. 294, pp. 120.
Global solutions to a onedimensional nonlinear wave equation
derivable from a variational principle
Yanbo Hu, Guodong Wang
Abstract:
This article focuses on a onedimensional nonlinear wave equation which
is the EulerLagrange 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 energydependent 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;
energydependent 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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