[Attracteurs semimartingales pour des EDPS d'Allen–Cahn généralisées dirigées par le bruit blanc spatio–temporel]
Nous introduisons la notion d'attracteur semimartingale associé aux EDPS d'Allen–Cahn généralisées dirigées par un bruit blanc spatio–temporel. Nous traitons notre bruit dans le cadre de mesure martingale, et nous donnons un résultat d'existence pour ce type d'attracteurs pour ces EDPS d'Allen–Cahn généralisées. Cette Note discute des attracteurs semimartingales fonctionnels, mais notre cadre du bruit mene aussi naturellement à un type lié d'attracteurs aléatoires que nous appelons attracteurs de mesure semimartingale et que nous détaillerons dans un prochain article. En outre, les preuves détaillées, avec d'autres propriétés d'attracteurs semimartingales et des extensions de notre resultat appliquées à différents types d'EDPS, seront aussi fournies dans ce prochain article.
We introduce the notion of a semimartingale attractor associated with space–time white noise driven generalized Allen–Cahn SPDEs. We treat the driving noise in the martingale measure setting, and we give an existence result for this type of random attractors for these generalized Allen–Cahn SPDEs in our setting. This Note focuses on semimartingale functional attractors, but our noise setting also leads naturally to a related type of random attractors that we call semimartingale measure attractors and which we detail in an upcoming article. Detailed proofs and extensions of our result, as well as other properties of semimartingale attractors, for different types of SPDEs are also furnished in the follow-up article.
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@article{CRMATH_2003__337_3_201_0,
author = {Allouba, Hassan and Langa, Jos\'e A.},
title = {Semimartingale attractors for generalized {Allen{\textendash}Cahn} {SPDEs} driven by space{\textendash}time white noise},
journal = {Comptes Rendus. Math\'ematique},
pages = {201--206},
publisher = {Elsevier},
volume = {337},
number = {3},
year = {2003},
doi = {10.1016/S1631-073X(03)00312-1},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(03)00312-1/}
}
TY - JOUR AU - Allouba, Hassan AU - Langa, José A. TI - Semimartingale attractors for generalized Allen–Cahn SPDEs driven by space–time white noise JO - Comptes Rendus. Mathématique PY - 2003 SP - 201 EP - 206 VL - 337 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(03)00312-1/ DO - 10.1016/S1631-073X(03)00312-1 LA - en ID - CRMATH_2003__337_3_201_0 ER -
%0 Journal Article %A Allouba, Hassan %A Langa, José A. %T Semimartingale attractors for generalized Allen–Cahn SPDEs driven by space–time white noise %J Comptes Rendus. Mathématique %D 2003 %P 201-206 %V 337 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(03)00312-1/ %R 10.1016/S1631-073X(03)00312-1 %G en %F CRMATH_2003__337_3_201_0
Allouba, Hassan; Langa, José A. Semimartingale attractors for generalized Allen–Cahn SPDEs driven by space–time white noise. Comptes Rendus. Mathématique, Tome 337 (2003) no. 3, pp. 201-206. doi : 10.1016/S1631-073X(03)00312-1. http://archive.numdam.org/articles/10.1016/S1631-073X(03)00312-1/
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