Nonexistence of global solutions of a quasilinear hyperbolic equation


Bayrak V., Can M., Aliyev F.

MATHEMATICAL INEQUALITIES & APPLICATIONS, vol.1, no.3, pp.367-374, 1998 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 1 Issue: 3
  • Publication Date: 1998
  • Title of Journal : MATHEMATICAL INEQUALITIES & APPLICATIONS
  • Page Numbers: pp.367-374

Abstract

In this work, the nonexistence of the global solutions to a class of initial boundary value problems with dissipative terms in the boundary conditions is considered for a quasilinear hyperbolic equation. The nonexistence proof is achieved by the use of a lemma due to O. Ladyzhenskaya and V. K. Kalantarov and 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 proves that this functional satisfies the hypotheses of Ladyzhenskaya-Kalantarov lemma. Hence from the conclusion of the lemma one concludes that in finite time t(2), this functional and hence the norm of the solution blows up.