Journal of Applied Mathematics and Computing

, Volume 38, Issue 1, pp 467–487

Global well-posedness for semilinear hyperbolic equations with dissipative term


DOI: 10.1007/s12190-011-0491-2

Cite this article as:
Jiang, X. & Xu, R. J. Appl. Math. Comput. (2012) 38: 467. doi:10.1007/s12190-011-0491-2


We study the initial boundary value problem of semilinear hyperbolic equations with dissipative term. By introducing a family of potential wells we derive the invariant sets and vacuum isolating of solutions. Then we prove the global existence, nonexistence and asymptotic behaviour of solutions. In particular we obtain some sharp conditions for global existence and nonexistence of solutions.


Semilinear hyperbolic equationPotential wellsGlobal existenceNonexistenceAsymptotic behaviour

Mathematics Subject Classification (2000)


Copyright information

© Korean Society for Computational and Applied Mathematics 2011

Authors and Affiliations

  1. 1.College of ScienceHarbin Engineering UniversityHarbinPeople’s Republic of China