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Invariant measure and large time dynamics of the cubic Klein-Gordon equation in $3D$ by Sy, Mouhamadou is a scholarly article available to read on EtoBox.

What is Invariant measure and large time dynamics of the cubic Klein-Gordon equation in $3D$ about?

In this paper we construct an invariant probability measure concentrated on $H^2(K)\times H^1(K)$ for a general cubic Klein-Gordon equation (including the case of the wave equation). Here $K$ represents both the $3$-dimensional torus or a bounded domain with smooth boundary in $\Bbb R^3.$ That allows to deduce some corollaries on the long time behaviour of the flow of the equation in a probabilistic sense. We also establish qualitative properties of the constructed measure. This work extends the Fluctuation-Dissipation-Limit (FDL) approach to PDEs having only one (coercive) conservation law.

Author

Sy, Mouhamadou

Published

2017

Language

EN