On periodic solutions of the Benjamin-Bona-Mahony-Burgers equation

Abstract

In this paper, we would establish the existence and stability of periodic solutions to the Benjamin-Bona-Mahony-Burgers (BBM-Burgers) equation in $H_0^1([0,1])$, whose medium interior is applied with time-periodic force $f(x,t)$ with period $\theta$. High regularity analysis has been conducted in Hilbert spaces $H^{\ell },\ell >1$. We also consider periodic solution to same IBVP scenario of a pseudo-parabolic-regularized equation as an extension of the BBM-Burgers in ${\mathcal{H}}^{\ell },\ell =\{1,2\}$.