A note on weak and strong probabilistic solutions for a stochastic quasilinear parabolic equation of generalized polytropic filtration

作者：Ali Zakaria Idriss^*; Sango Mamadou

来源：International Journal of Modern Physics B, 2016, 30(28-29): 1640002.

DOI：10.1142/S0217979216400026

• SPDEs
• nonstandard growth
• monotonicity

In this paper, we investigate a class of stochastic quasilinear parabolic problems with nonstandard growth in the functional setting of generalized Sobolev spaces. The deterministic version of the equation was first introduced and studied by Samokhin, as a generalized model for polytropic filtration. We establish an existence result of weak probabilistic solutions when the forcing terms do not satisfy Lipschitz conditions. Under Lipschitzity of the nonlinear external forces, f and G, we obtain the uniqueness of the weak probabilistic solutions. Combining the uniqueness and the famous Yamada- Watanabe result we prove the existence of the unique strong probabilistic solution.

• 出版日期2016-11-20