Nonexistence of global solutions of a quasilinear hyperbolic equation


Bayrak V., Can M., Aliyev F.

MATHEMATICAL INEQUALITIES & APPLICATIONS, cilt.1, sa.3, ss.367-374, 1998 (SCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 1 Konu: 3
  • Basım Tarihi: 1998
  • Dergi Adı: MATHEMATICAL INEQUALITIES & APPLICATIONS
  • Sayfa Sayıları: ss.367-374

Özet

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.