ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35 Can, Mehmet and Bayrak Vural, Istanbul Technical University, Turkiye Blow up of solutions of a quasilinear hyperbolic equation with applications In this work, the nonexistence of the global solutions of initial boundary value problems are considered for a class of quasilinear hyperbolic equations:

u_{tt} − Δu + aΔ^{2}u + bΔf(u) = 0, (t, x) ∈ (0, T) × Ω
u(x, 0) = u_{0}(x), u_{t}(x, 0) = u_{1}(x) x ∈ Ω

with dissipative terms in several different boundary conditions where Ω is a bounded domain in R^{n} with a sufficiently smooth boundary Γ, T > 0 is an arbitrary real number. The nonexistence proof is achieved by the use of the so called concavity method.