[EDSR multidimensionnelles à croissance surlinéaire : Application aux systèmes d'EDP dégénérées]
Nous établissons l'existence, l'unicité et la stability des solutions fortes pour des équations différentielles stochastiques rétrogrades (EDSR) avec une condition terminale p-integrable et un coefficient admettant des croissances surlinéaires en les deux variables y et z. De plus, ce dernier peut être ni locallement monotone en y ni localement Lipschitz en z. Nous montrons également l'existence et l'unicité des solutions faibles pour les systèmes d'EDP associés. L'uniforme ellipticité n'est pas requise pour la matrice de diffusion.
We establish the existence and uniqueness as well as the stability of p-integrable solutions to multidimensional backward stochastic differential equations (BSDEs) with super-linear growth coefficient and a p-integrable terminal condition . The generator could neither be locally monotone in the variable y nor locally Lipschitz in the variable z. As application, we establish the existence and uniqueness of weak (Sobolev) solutions to the associated systems of semilinear parabolic PDEs. The uniform ellipticity of the diffusion matrix is not required. Our result covers, for instance, certain systems of PDEs with logarithmic nonlinearities which arise in physics.
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@article{CRMATH_2010__348_11-12_677_0,
author = {Bahlali, K. and Essaky, E. and Hassani, M.},
title = {Multidimensional {BSDEs} with super-linear growth coefficient: {Application} to degenerate systems of semilinear {PDEs}},
journal = {Comptes Rendus. Math\'ematique},
pages = {677--682},
publisher = {Elsevier},
volume = {348},
number = {11-12},
year = {2010},
doi = {10.1016/j.crma.2010.03.006},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.03.006/}
}
TY - JOUR AU - Bahlali, K. AU - Essaky, E. AU - Hassani, M. TI - Multidimensional BSDEs with super-linear growth coefficient: Application to degenerate systems of semilinear PDEs JO - Comptes Rendus. Mathématique PY - 2010 SP - 677 EP - 682 VL - 348 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.03.006/ DO - 10.1016/j.crma.2010.03.006 LA - en ID - CRMATH_2010__348_11-12_677_0 ER -
%0 Journal Article %A Bahlali, K. %A Essaky, E. %A Hassani, M. %T Multidimensional BSDEs with super-linear growth coefficient: Application to degenerate systems of semilinear PDEs %J Comptes Rendus. Mathématique %D 2010 %P 677-682 %V 348 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.03.006/ %R 10.1016/j.crma.2010.03.006 %G en %F CRMATH_2010__348_11-12_677_0
Bahlali, K.; Essaky, E.; Hassani, M. Multidimensional BSDEs with super-linear growth coefficient: Application to degenerate systems of semilinear PDEs. Comptes Rendus. Mathématique, Tome 348 (2010) no. 11-12, pp. 677-682. doi : 10.1016/j.crma.2010.03.006. http://www.numdam.org/articles/10.1016/j.crma.2010.03.006/
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