Nonexistence of Global Solutions of Some Quasilinear Hyperbolic Equations

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