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Chapitre D'ouvrage Année : 2019

Blow-up rate for a semilinear wave equation with exponential nonlinearity in one space dimension

Résumé

We consider in this paper blow-up solutions of the semilinear wave equation in one space dimension, with an exponential source term. Assuming that initial data are in $H^{1}_{loc}\times L^2_{loc}$ or some times in $ W^{1,\infty}\times L^{\infty}$, we derive the blow-up rate near a non-characteristic point in the smaller space, and give some bounds near other points. Our result generalize those proved by Godin under high regularity assumptions on initial data.

Dates et versions

hal-02325078 , version 1 (22-10-2019)

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Citer

Asma Azaiez, Nader Masmoudi, Hatem Zaag. Blow-up rate for a semilinear wave equation with exponential nonlinearity in one space dimension. Mohamed Ben Ayed. Partial Differential Equations arising from Physics and Geometry, Cambridge University Press, 2019. ⟨hal-02325078⟩
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