ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35L70 Katayama, Soichiro, Wakayama University, Japan Some semilinear wave equations with nonlinear damping terms. We consider the Cauchy or mixed problems for u_{tt}−Δu+Q(u, u_{t}) = |u|^{p−1}u in (0, ∞) × Ω, where Ω ⊂ R^{n} and 1 < p < ∞. Here Q is a nonlinear damping term. In the case when Ω ≠ R^{n}, we impose the Dirichlet boundary condition. When Q = |u_{t}|^{m−1}u_{t} with 1 < m < ∞, conditions for global existence and blow-up of a weak solution were derived by Georgiev and Todorova. We consider the case when Q = |u|^{m−1}u_{t} with 1 < m < ∞ and n = 1, and the conditions for global existence and blow-up of solutions will be presented. This result is joint work with Md. Abu Naim Sheikh and S. Tarama. References: V. Georgiev and G. Todorova, Existence of a solution of the wave equation with nonlinear damping and source terms, J. of Diff. Eqs. 109 (1994), 295–308.