Continuity of the flow of the Benjamin-Bona-Mahony equation on probability measures
Anne-Sophie de Suzzoni
TL;DR
This paper investigates how the flow of the Benjamin-Bona-Mahony (BBM) equation acts on probability measures using Wasserstein metrics, establishing flow continuity and invariant measure stability over finite times.
Contribution
It introduces a Wasserstein metric framework to analyze the BBM flow on probability measures, proving continuity and stability results not previously established.
Findings
Flow of BBM is continuous in Wasserstein metric
Invariant measures are stable over finite times
Provides a new analytical approach for measure evolution under BBM
Abstract
We use Wasserstein metrics adapted to study the action of the flow of the BBM equation on probability measures. We prove the continuity of this flow and the stability of invariant measures for finite times.
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