Comptes Rendus
no. 3-4
Ordinary Differential Equations/Partial Differential Equations
On an explicit representation of the solution of linear stochastic partial differential equations with delays

Presented by: Jean-Michel Bony

Mathieu Galtier1; Jonathan Touboul2
1 NeuroMathComp Project Team, INRIA, 23, avenue dʼItalie, 75013 Paris, France
2 The Mathematical Neuroscience Laboratory, CIRB/Collège de France (CNRS UMR 7241, INSERM U1050, UPMC ED 158, MEMOLIFE PSL
Comptes Rendus. Mathématique, Volume 350 (2012) no. 3-4, pp. 167-172.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.01.004

Mathieu Galtier 1; Jonathan Touboul 2

1 NeuroMathComp Project Team, INRIA, 23, avenue dʼItalie, 75013 Paris, France
2 The Mathematical Neuroscience Laboratory, CIRB/Collège de France (CNRS UMR 7241, INSERM U1050, UPMC ED 158, MEMOLIFE PSL 
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Mathieu Galtier; Jonathan Touboul. On an explicit representation of the solution of linear stochastic partial differential equations with delays. Comptes Rendus. Mathématique, Volume 350 (2012) no. 3-4, pp. 167-172. doi : 10.1016/j.crma.2012.01.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.01.004/

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