Electron. J. Diff. Eqns., Vol. 2003(2003), No. 30, pp. 1-17.

A nonlocal mixed semilinear problem for second-order hyperbolic equations

Said Mesloub & Salim A. Messaoudi

In this work we study a nonlinear hyperbolic one-dimensional problem with a nonlocal condition. We establish a blow up result for large initial data and a decay result for small initial data.

Submitted January 2, 2003. Published March 17, 2003.
Math Subject Classifications: 35L20, 35L67.
Key Words: Semilinear hyperbolic equation, integral condition, strong solution, existnece, uniqueness, blow up, decay.

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Said Mesloub
Departement de Mathematiques
Universite de Tebessa
Tebessa 12002, Algerie
email: mesloubs@hotmail.com
Salim A. Messaoudi
Departement of Mathematics
King Fahd University of Petroleum & Menirals
Dahran 31261, Saudia Arabia
e-mail: messaoud@kfupm.edu.sa

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