Journal of Applied Mathematics and Computing

, Volume 38, Issue 1, pp 467–487

Global well-posedness for semilinear hyperbolic equations with dissipative term

Authors

  • Xiaoli Jiang
    • College of ScienceHarbin Engineering University
    • College of ScienceHarbin Engineering University
Article

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

Abstract

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.

Keywords

Semilinear hyperbolic equationPotential wellsGlobal existenceNonexistenceAsymptotic behaviour

Mathematics Subject Classification (2000)

35L25

Copyright information

© Korean Society for Computational and Applied Mathematics 2011