Abstract
In this paper, we establish the Freidlin-Wentzell type large deviation principle for porous medium-type equations perturbed by small multiplicative noise. The porous medium operator $\Delta (|u|^{m-1}u)$ is allowed. Our proof is based on weak convergence approach.
Highlights
We are interested in the asymptotic behaviour of porous media equations with small multiplicative noise
We are concerned with the following porous media equations with stochastic forcing du(t, x) = ∆(|u(t, x)|m−1u(t, x))dt + Φ(u(t, x))dW (t) in TN × (0, T ], u(·, 0) = u0(·) ∈ Lm+1(TN ) on TN, (1.1)
The purpose of this paper is to prove that the kinetic solution to the stochastic porous mediumtype equations (1.2) satisfies Freidlin-Wentzell type large deviation principle (LDP) in the space L1([0, T ]; L1(TN )), which is a more delicate result compared with [29] and [23]
Summary
We are interested in the asymptotic behaviour of porous media equations with small multiplicative noise. The purpose of this paper is to prove that the kinetic solution to the stochastic porous mediumtype equations (1.2) satisfies Freidlin-Wentzell type LDP in the space L1([0, T ]; L1(TN )), which is a more delicate result compared with [29] and [23]. The present paper is the first work towards establishing the LDP directly for the kinetic solution to the stochastic porous medium-type equations (1.2). Due to the fact that the kinetic solutions are living in a rather irregular space comparing to various type solutions for parabolic SPDEs, it is a challenge to establish LDP for the stochastic porous media equations with general noise force.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
