Strong Solutions of Stochastic Generalized Porous Media Equations : Existence , Uniqueness and Ergodicity ∗
نویسندگان
چکیده
Explicit conditions are presented for the existence, uniqueness and ergodicity of the strong solution to a class of generalized stochastic porous media equations. Our estimate of the convergence rate is sharp according to the known optimal decay for the solution of the classical (deterministic) porous medium equation. AMS subject Classification: 76S05, 60H15.
منابع مشابه
Non-Monotone Stochastic Generalized Porous Media Equations∗
By using the Nash inequality and a monotonicity approximation argument, existence and uniqueness of strong solutions are proved for a class of non-monotone stochastic generalized porous media equations. Moreover, we prove for a large class of stochastic PDE that the solutions stay in the smaller L2-space provided the initial value does, so that some recent results in the literature are consider...
متن کاملExistence of strong solutions for stochastic porous media equation under general monotonicity conditions
One proves existence and uniqueness of strong solutions to stochastic porous media equations under minimal monotonicity conditions on the nonlinearity. In particular, we do not assume continuity of the drift or any growth condition at infinity. AMS subject Classification 2000: 76S05, 60H15. Supported by the CEEX Project 05 of Romanian Minister of Research. Supported by the research program “Equ...
متن کاملStochastic porous media equation and self-organized criticality
The existence and uniqueness of nonnegative strong solutions for stochastic porous media equations with noncoercive monotone diffusivity function and Wiener forcing term is proven. The finite time extinction of solutions with high probability is also proven in 1-D. The results are relevant for self-organized critical behaviour of stochastic nonlinear diffusion equations with critical states. AM...
متن کاملConcentration of Invariant Measures for Stochastic Generalized Porous Media Equations
By using Bernstein functions, existence and concentration properties are studied for invariant measures of the infinitesimal generators associated to a large class of stochastic generalized porous media equations. In particular, results derived in [4] are extended to equations with non-constant and stronger noises. Analogous results are also proved for invariant probability measures for strong ...
متن کاملStochastic Tamed 3d Navier-stokes Equations: Existence, Uniqueness and Ergodicity
In this paper, we prove the existence of a unique strong solution to a stochastic tamed 3D Navier-Stokes equation in the whole space as well as in the periodic boundary case. Then, we also study the Feller property of solutions, and prove the existence of invariant measures for the corresponding Feller semigroup in the case of periodic conditions. Moreover, in the case of periodic boundary and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008