[Une expression analytique pour la solution dʼéquations aux dérivées partielles linéaires stochastiques avec délais]
En se basant sur lʼanalyse dʼune certaine classe dʼopérateurs linéraires dans des espaces de Banach, nous établissons une expression analytique pour la solution de certaines équations aux dérivées partielles linéaires avec des entrées non-autonomes, des délais et des termes stochastique, sous la forme dʼun développement en série.
Based on the analysis of a certain class of linear operators on a Banach space, we provide a closed form expression for the solutions of certain linear partial differential equations with non-autonomous input, time delays and stochastic terms, which takes the form of an infinite series expansion.
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@article{CRMATH_2012__350_3-4_167_0,
author = {Galtier, Mathieu and Touboul, Jonathan},
title = {On an explicit representation of the solution of linear stochastic partial differential equations with delays},
journal = {Comptes Rendus. Math\'ematique},
pages = {167--172},
publisher = {Elsevier},
volume = {350},
number = {3-4},
year = {2012},
doi = {10.1016/j.crma.2012.01.004},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.01.004/}
}
TY - JOUR AU - Galtier, Mathieu AU - Touboul, Jonathan TI - On an explicit representation of the solution of linear stochastic partial differential equations with delays JO - Comptes Rendus. Mathématique PY - 2012 SP - 167 EP - 172 VL - 350 IS - 3-4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.01.004/ DO - 10.1016/j.crma.2012.01.004 LA - en ID - CRMATH_2012__350_3-4_167_0 ER -
%0 Journal Article %A Galtier, Mathieu %A Touboul, Jonathan %T On an explicit representation of the solution of linear stochastic partial differential equations with delays %J Comptes Rendus. Mathématique %D 2012 %P 167-172 %V 350 %N 3-4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.01.004/ %R 10.1016/j.crma.2012.01.004 %G en %F CRMATH_2012__350_3-4_167_0
Galtier, Mathieu; Touboul, Jonathan. On an explicit representation of the solution of linear stochastic partial differential equations with delays. Comptes Rendus. Mathématique, Tome 350 (2012) no. 3-4, pp. 167-172. doi : 10.1016/j.crma.2012.01.004. http://www.numdam.org/articles/10.1016/j.crma.2012.01.004/
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