We prove the existence of a weak mild solution (or mild solution-measure) to the Cauchy problem for the semilinear stochastic differential inclusion in a Hilbert space where W is a cylindrical Wiener process, A is a linear operator which generates a -semigroup, F and G are multifunctions with convex compact values satisfying a linear growth condition and a condition weaker than the Lipschitz condition. The weak solution is constructed in the sense of Young measures. In the case when F and G are single-valued, we obtain the existence of a strong solution.
Nous démontrons l'existence d'une solution d'évolution faible (ou solution-mesure d'évolution) de l'inclusion différentielle stochastique dans un espace de Hilbert où W est un mouvement brownien cylindrique, A est un opérateur linéaire qui engendre un semi-groupe de classe , F et G sont des multifonctions à valeurs convexes compactes vérifiant une condition de croissance linéaire ainsi qu'une condition plus générale que la condition de Lipschitz. La solution faible est construite au sens des mesures de Young. Lorsque F et G sont univoques, on obtient l'existence d'une solution forte.
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Adam Jakubowski 1; Mikhail I. Kamenskiı̆ 2; Paul Raynaud de Fitte 3
@article{CRMATH_2005__340_3_229_0, author = {Adam Jakubowski and Mikhail I. Kamenski{\i}̆ and Paul Raynaud de Fitte}, title = {Existence of weak solutions to stochastic evolution inclusions}, journal = {Comptes Rendus. Math\'ematique}, pages = {229--234}, publisher = {Elsevier}, volume = {340}, number = {3}, year = {2005}, doi = {10.1016/j.crma.2004.12.015}, language = {en}, }
TY - JOUR AU - Adam Jakubowski AU - Mikhail I. Kamenskiı̆ AU - Paul Raynaud de Fitte TI - Existence of weak solutions to stochastic evolution inclusions JO - Comptes Rendus. Mathématique PY - 2005 SP - 229 EP - 234 VL - 340 IS - 3 PB - Elsevier DO - 10.1016/j.crma.2004.12.015 LA - en ID - CRMATH_2005__340_3_229_0 ER -
Adam Jakubowski; Mikhail I. Kamenskiı̆; Paul Raynaud de Fitte. Existence of weak solutions to stochastic evolution inclusions. Comptes Rendus. Mathématique, Volume 340 (2005) no. 3, pp. 229-234. doi : 10.1016/j.crma.2004.12.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.12.015/
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