Global weak solutions to a generalized Benjamin-Bona-Mahony-Burgers equation

The existence of global weak solutions for a generalized Benjamin-Bona-Mahony-Burgers equation is established in the space $C\left([0,\infty )\times R)\cap L^{\infty }\left([0,\infty \right);H^1\left(R\right)\right)$ under the condition that its initial value belongs to the space H¹(R). A one-sided super bound estimate and a space-time higher-norm estimate on the first order derivatives of the solution with respect to the space variable are derived to prove the existence.