Markovianity and ergodicity for a surface growth PDE

2006/11/01 by D. Blömker, Dirk Blömker, Franco Flandoli +6
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.MP #math.PR #msc:35Q99 #msc:35R60 #msc:60H15 #msc:60H30

paper · pdf · doi:10.48550/arxiv.math/0611021

33 pages, 1 figure

arxiv created 2006/11/01 · arxiv updated 2009/12/01

Abstract

The paper analyses a model in surface growth, where uniqueness of weak solutions seems to be out of reach. We provide the existence of a weak martingale solution satisfying energy inequalities and having the Markov property. Furthermore, under non-degeneracy conditions on the noise, we establish that any such solution is strong Feller and has a unique invariant measure.

Related

• Local existence and uniqueness in the largest critical space for a surface growth model
• An almost sure energy inequality for Markov solutions to the 3D Navier-Stokes equations
• Exponential ergodicity of the solutions to SDE's with a jump noise
• The strong Feller property for singular stochastic PDEs
• Local existence and uniqueness for a two-dimensional surface growth equation with space--time white noise