Ergodicity for singular-degenerate porous media equations

Abstract

The long time behaviour of solutions to generalised stochastic porous media equations on bounded domains with Dirichlet boundary data is studied. We focus on a degenerate form of nonlinearity arising in self-organised criticality. Based on the so-called lower-bound method, the existence and uniqueness of an invariant measure is proved.

References in corpus (4)

• Random attractors for a class of stochastic partial differential equations driven by general additive noise
• Harnack inequality and applications for stochastic generalized porous media equations
• Couplings via comparison principle and exponential ergodicity of SPDEs in the hypoelliptic setting
• Ergodicity for Stochastic Porous Media Equations

Cited by in corpus (1)

• Well-posedness of SVI solutions to singular-degenerate stochastic porous media equations arising in self-organised criticality