Long time existence results for bore-type initial data for BBM-Boussinesq systems

TL;DR

This paper establishes long time existence results for BBM-Boussinesq systems with initial data modeling bore propagation, extending previous work to include nontrivial behavior at infinity.

Contribution

It introduces long time existence results for initial data with nontrivial behavior at infinity in BBM-Boussinesq systems, relevant for bore wave modeling.

Findings

Proves long time existence for bore-type initial data

Extends previous models to include nontrivial behavior at infinity

Provides mathematical foundation for bore wave propagation modeling

Abstract

In this paper we deal with the long time existence for the Cauchy problem associated to BBM-type Boussinesq systems of equations which are asymptotic models for long wave, small amplitude gravity surface water waves. As opposed to previous papers devoted to the long time existence issue, we consider initial data with nontrivial behaviour at innity which may be used to model bore propagation.