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Zeitschrift für Analysis und ihre Anwendungen


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Volume 19, Issue 2, 2000, pp. 453–468
DOI: 10.4171/ZAA/961

Published online: 2000-06-30

Non-Existence Results for a Semilinear Hyperbolic Problem with Boundary Condition of Memory Type

Mokhtar Kirane[1] and Nasser-edine Tatar[2]

(1) Université de la Rochelle, France
(2) King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

We consider a problem which models the evolution of sound in a compressible fluid with reflection of sound at the surface of the material. Different methods such as the concavity method of Levine, the potential well method and an argument due to Tsutsumi are used to derive global non-existence theorems.

Keywords: Semilinear hyperbolic equations, blow-up in finite time

Kirane Mokhtar, Tatar Nasser-edine: Non-Existence Results for a Semilinear Hyperbolic Problem with Boundary Condition of Memory Type. Z. Anal. Anwend. 19 (2000), 453-468. doi: 10.4171/ZAA/961