Approach to Equilibrium for a Forced Burgers Equation

TL;DR

This paper demonstrates how the approach to equilibrium in certain forced Burgers equations can be established through decay estimates of an intrinsic semigroup, verified across various cases including periodic forcing.

Contribution

It introduces a method linking decay estimates of semigroups to equilibrium approach in forced Burgers equations, including cases with periodic forcing.

Findings

Decay estimates imply approach to equilibrium.

Verification of estimates in periodic forcing scenarios.

Extension of method to various forcing cases.

Abstract

We show that approach to equilibrium in certain forced Burgers equations is implied by a decay estimate on a suitable intrinsic semigroup estimate, and we verify this estimate in a variety of cases including a periodic force.