[EDP non-locales avec terme à retards dépendants de l'état exprimé par une intégrale de Stieltjes]
On étudie des équations aux dérivées partielles avec des retards dépendants de l'état (RDE). Le terme comportant les retards est exprimé par une intégrale de Stieltjes incluant des RDE discrets et distribués. Une mesure de Lebesgue–Stieltjes singulière est aussi admissible. On présente des conditions pour que le problème de Cauchy soit bien posé. On montre l'existence d'un attracteur global compact.
Parabolic partial differential equations with state-dependent delays (SDDs) are investigated. The delay term presented by Stieltjes integral simultaneously includes discrete and distributed SDDs. The singular Lebesgue–Stieltjes measure is also admissible. The conditions for the corresponding initial value problem to be well-posed are presented. The existence of a compact global attractor is proved.
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@article{CRMATH_2011__349_3-4_179_0,
author = {Rezounenko, Alexander V.},
title = {Non-local {PDEs} with a state-dependent delay term presented by {Stieltjes} integral},
journal = {Comptes Rendus. Math\'ematique},
pages = {179--183},
publisher = {Elsevier},
volume = {349},
number = {3-4},
year = {2011},
doi = {10.1016/j.crma.2011.01.012},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.01.012/}
}
TY - JOUR AU - Rezounenko, Alexander V. TI - Non-local PDEs with a state-dependent delay term presented by Stieltjes integral JO - Comptes Rendus. Mathématique PY - 2011 SP - 179 EP - 183 VL - 349 IS - 3-4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.01.012/ DO - 10.1016/j.crma.2011.01.012 LA - en ID - CRMATH_2011__349_3-4_179_0 ER -
%0 Journal Article %A Rezounenko, Alexander V. %T Non-local PDEs with a state-dependent delay term presented by Stieltjes integral %J Comptes Rendus. Mathématique %D 2011 %P 179-183 %V 349 %N 3-4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.01.012/ %R 10.1016/j.crma.2011.01.012 %G en %F CRMATH_2011__349_3-4_179_0
Rezounenko, Alexander V. Non-local PDEs with a state-dependent delay term presented by Stieltjes integral. Comptes Rendus. Mathématique, Tome 349 (2011) no. 3-4, pp. 179-183. doi : 10.1016/j.crma.2011.01.012. http://www.numdam.org/articles/10.1016/j.crma.2011.01.012/
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