Forced oscillation of a damped BBM equation posed on whole line in low regularity spaces

TL;DR

This paper proves the existence and stability of time-periodic solutions for a forced damped BBM equation on the whole line in low regularity spaces, advancing understanding of nonlinear wave equations in less smooth contexts.

Contribution

It establishes the existence and stability of solutions in low regularity spaces for the forced damped BBM equation, using I-energy estimates and perturbation methods.

Findings

Existence of time-periodic solutions in $H^ ell$ spaces.

Stability results for these solutions.

Application of I-energy method to low regularity analysis.

Abstract

In this manuscript, we would established in low regularity spaces $H^\ell, \ell\in [0,1)$, the existence and stability results of time-periodic solution of 1D Cauchy problem of forced damped Benjamin-Bona-Mahony equation (BBM). We use estimates from I-energy method to derive needed estimates in $H^\ell$ for the linearized problem, then convection term will be treated as perturbation of linear problem such that original Cauchy problem is solved.