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.
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Mokhtar Kirane, Nasser-edine Tatar, Non-Existence Results for a Semilinear Hyperbolic Problem with Boundary Condition of Memory Type. Z. Anal. Anwend. 19 (2000), no. 2, pp. 453–468DOI 10.4171/ZAA/961