Full paper in PDF:
$%M. Kirane and S. A. Messaoudi, Breakdown in finite time of solutions to a one-dimensional wave equation, Rev. Mat. Complut. 13 (2000), no. 2, 422–413.%$

Breakdown in Finite Time of Solutions to a One-Dimensional Wave Equation
Mokhtar KIRANE and Salim A. MESSAOUDI
Math. Sciences Department
KFUPM
Dhahrah 31261 — Saudi Arabia
messaoud@kfupm.edu.sa

Received: February 8, 1999
Revised: March 8, 2000

ABSTRACT

We consider a special type of a one-dimensional quasilinear wave equation wt wtt- f(wx)wxx in a bounded domain with Dirichlet boundary conditions and show that classical solutions blow up in finite time even for small initial data in some norm.

1991 Mathematics Subject Classification: 35L45.