[Un principe du maximum pour les solutions bornées de l'équation des télégraphistes en dimension spatiale trois]
On démontre un principe du maximum pour les solutions faibles de l'équation des télégraphistes utt−Δxu+cut+λu=f(t,x) en dimension spatiale trois lorsque c>0, λ∈(0,c2/4] et (Théorème 1). Le résultat est étendu à une solution et un terme forçant appartenant à un certain espace de mesures bornées (Théorème 2). Ces résultats fournissent une méthode de sous- et sur-solutions pour l'équation semilinéaire utt−Δxu+cut=F(t,x,u).
A maximum principle is proved for the weak solutions of the telegraph equation utt−Δxu+cut+λu=f(t,x), in space dimension three, when c>0, λ∈(0,c2/4] and (Theorem 1). The result is extended to a solution and a forcing belonging to a suitable space of bounded measures (Theorem 2). Those results provide a method of upper and lower solutions for the semilinear equation utt−Δxu+cut=F(t,x,u).
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@article{CRMATH_2002__334_12_1089_0,
author = {Mawhin, Jean and Ortega, Rafael and Robles-P\'erez, Aureliano M.},
title = {A maximum principle for bounded solutions of the telegraph equation in space dimension three},
journal = {Comptes Rendus. Math\'ematique},
pages = {1089--1094},
publisher = {Elsevier},
volume = {334},
number = {12},
year = {2002},
doi = {10.1016/S1631-073X(02)02406-8},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02406-8/}
}
TY - JOUR AU - Mawhin, Jean AU - Ortega, Rafael AU - Robles-Pérez, Aureliano M. TI - A maximum principle for bounded solutions of the telegraph equation in space dimension three JO - Comptes Rendus. Mathématique PY - 2002 SP - 1089 EP - 1094 VL - 334 IS - 12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02406-8/ DO - 10.1016/S1631-073X(02)02406-8 LA - en ID - CRMATH_2002__334_12_1089_0 ER -
%0 Journal Article %A Mawhin, Jean %A Ortega, Rafael %A Robles-Pérez, Aureliano M. %T A maximum principle for bounded solutions of the telegraph equation in space dimension three %J Comptes Rendus. Mathématique %D 2002 %P 1089-1094 %V 334 %N 12 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02406-8/ %R 10.1016/S1631-073X(02)02406-8 %G en %F CRMATH_2002__334_12_1089_0
Mawhin, Jean; Ortega, Rafael; Robles-Pérez, Aureliano M. A maximum principle for bounded solutions of the telegraph equation in space dimension three. Comptes Rendus. Mathématique, Tome 334 (2002) no. 12, pp. 1089-1094. doi : 10.1016/S1631-073X(02)02406-8. http://www.numdam.org/articles/10.1016/S1631-073X(02)02406-8/
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