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## Benjamin-Bona-Mahony-Burgers type equations (BBMB)

The original Benjamin-Bona-Mahoni equation is given as follows:
This equation has been proposed as a model for propagation of long waves. Here  is a positive constant and  is typically the amplitude or velocity.  describes the distance in the direction of propagation. This equation incorporates dispersive and dissipative effects. The dissipative term is just expressed by . The equation without dissipative term is called Benjamin-Bona-Mahony equation. The first paper in this field has been written by Benjamin, R.T., Bona J.L. and Mahony, J.J. in 1972 . The title of this paper was Model equations for long waves in nonlinear dispersiv systems (Philos. Trans. Roy. Soc. London, 272, 47-78). BBMB can be seen as an alternative model for the Korteweg-de Vries equation. Nowadays were studied generalizations as :
where  and  is a bounded interval. We have a initial condition
In many cases the boundary condition is assumed periodically. This equation belongs to the Sobolev-Galpern type equations.

A late Reference:: B. Wang: Attractors and Approximate Inertial Manifolds for the generalized BBME, MMAS, 20, 3 (1997)

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collected and worked out by Wolfgang Sprößig, TU-Bergakademie Freiberg