Nonexistence of global solutions of some quasilinear hyperbolic equations


Can M., Park S., Aliyev F.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.213, no.2, pp.540-553, 1997 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 213 Issue: 2
  • Publication Date: 1997
  • Doi Number: 10.1006/jmaa.1997.5557
  • Title of Journal : JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Page Numbers: pp.540-553

Abstract

in this work, the nonexistence of the global solutions to initial boundary value problems with dissipative terms in the boundary conditions is considered for a class of quasilinear hyperbolic equations. The nonexistence proof is achieved by the usage of the so-called concavity method. In this method one writes down a functional which reflects the properties of dissipative boundary conditions and represents the norm of the solution in some sense. Then it is proved that this functional satisfies the hypotheses of the concavity lemma. Hence from the conclusion of the lemma one concludes that this functional and hence the norm of the solution blows up in a finite time. (C) 1997 Academic Press.