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Finite Time Blow-Up for Wave Equations with Strong Damping in an Exterior Domain

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Abstract

We consider the initial boundary value problem in exterior domain for strongly damped wave equations with power-type nonlinearity \(|u|^p\). We will establish blow-up results under some conditions on the initial data and the exponent p, using the method of test function with an appropriate harmonic functions. We also study the existence of mild solution and its relation with the weak formulation.

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Acknowledgements

The author would like to express sincere gratitude to Professor Ryo Ikehata for valuable discussion. The referee deserves thanks for careful reading and many useful comments leading to improvement of the paper.

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  1. Department of Mathematics, Faculty of Sciences, Lebanese University, P.O. Box 1352, Tripoli, Lebanon

    Ahmad Z. Fino

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  1. Ahmad Z. Fino
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Correspondence to Ahmad Z. Fino.

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Fino, A.Z. Finite Time Blow-Up for Wave Equations with Strong Damping in an Exterior Domain. Mediterr. J. Math. 17, 174 (2020). https://doi.org/10.1007/s00009-020-01607-2

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  • DOI: https://doi.org/10.1007/s00009-020-01607-2

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