Nous prouvons l'extinction avec une probabilité strictement positive pour les solutions des équations des milieux poreux avec diffusion rapide.
We prove that the solutions to fast diffusion stochastic porous media equations have finite time extinction with strictly positive probability.
Accepté le :
Publié le :
@article{CRMATH_2009__347_1-2_81_0, author = {Barbu, Viorel and Da Prato, Giuseppe and R\"ockner, Michael}, title = {Finite time extinction for solutions to fast diffusion stochastic porous media equations}, journal = {Comptes Rendus. Math\'ematique}, pages = {81--84}, publisher = {Elsevier}, volume = {347}, number = {1-2}, year = {2009}, doi = {10.1016/j.crma.2008.11.018}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2008.11.018/} }
TY - JOUR AU - Barbu, Viorel AU - Da Prato, Giuseppe AU - Röckner, Michael TI - Finite time extinction for solutions to fast diffusion stochastic porous media equations JO - Comptes Rendus. Mathématique PY - 2009 SP - 81 EP - 84 VL - 347 IS - 1-2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2008.11.018/ DO - 10.1016/j.crma.2008.11.018 LA - en ID - CRMATH_2009__347_1-2_81_0 ER -
%0 Journal Article %A Barbu, Viorel %A Da Prato, Giuseppe %A Röckner, Michael %T Finite time extinction for solutions to fast diffusion stochastic porous media equations %J Comptes Rendus. Mathématique %D 2009 %P 81-84 %V 347 %N 1-2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2008.11.018/ %R 10.1016/j.crma.2008.11.018 %G en %F CRMATH_2009__347_1-2_81_0
Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael. Finite time extinction for solutions to fast diffusion stochastic porous media equations. Comptes Rendus. Mathématique, Tome 347 (2009) no. 1-2, pp. 81-84. doi : 10.1016/j.crma.2008.11.018. http://archive.numdam.org/articles/10.1016/j.crma.2008.11.018/
[1] Existence and uniqueness of nonnegative solutions to the stochastic porous media equation, Indiana Univ. Math. J., Volume 57 (2008), pp. 187-212
[2] V. Barbu, G. Da Prato, M. Röckner, Existence of strong solutions for stochastic porous media equation under general monotonicity conditions, Ann. Probab., in press
[3] V. Barbu, G. Da Prato, M. Röckner, Stochastic porous media equations and self-organized criticality, Comm. Math. Phys., in press
[4] Stability of the separable solution for fast diffusion, Arch. Rational Mech. Anal., Volume 74 (1980) no. 4, pp. 379-388
[5] Stochastic generalized porous media and fast diffusion equations, J. Differential Equations, Volume 238 (2007) no. 1, pp. 118-152
[6] M. Röckner, F.Y. Wang, Non-monotone stochastic generalized porous media equations, J. Differential Equations, in press
Cité par Sources :