Non existence de solutions globales de certaines équations d'ondes non linéaires
[Nonexistence of global solutions to some nonlinear wave equations]
Comptes Rendus. Mathématique, Volume 334 (2002) no. 11, pp. 961-966.

We study the semilinear wave equation uttΔu=pk|u|m in × n , where p is a conformal factor approaching 0 at infinity. We prove that the solutions blow-up in finite time for small powers m, while having an arbitrarily long life-span for large m. Furthermore, we study the finite time blow-up of solutions for the class of quasilinear wave equations uttΔu=pk|Lu|m in × n .

On étudie l'équation des ondes semi-linéaire uttΔu=pk|u|m dans × n , où p est un facteur conforme tendant vers 0 à l'infini. On montre que les solutions explosent en temps fini pour des petites puissances m, alors qu'elles ont un temps de vie arbitrairement long pour les m grands. De plus, on étudie l'explosion en temps fini des solutions de la classe d'équations des ondes quasilinéaires uttΔu=pk|Lu|m dans × n .

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DOI: 10.1016/S1631-073X(02)02355-5
Aassila, Mohammed 1

1 Institut de Mathématique, Université de Fribourg, Pérolles, CH-1700, Fribourg, Suisse
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     title = {Non existence de solutions globales de certaines \'equations d'ondes non lin\'eaires},
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Aassila, Mohammed. Non existence de solutions globales de certaines équations d'ondes non linéaires. Comptes Rendus. Mathématique, Volume 334 (2002) no. 11, pp. 961-966. doi : 10.1016/S1631-073X(02)02355-5. http://www.numdam.org/articles/10.1016/S1631-073X(02)02355-5/

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