On the blow-up of solutions of the Benjamin–Bona–Mahony–Burgers and Rosenau–Burgers equations

In this paper, we study sufficient conditions of the blow-up of solutions of initial–boundary-value problems for the well-known Benjamin–Bona–Mahony–Burgers and Rosenau–Burgers equations on a segment. Note that this is the first result for these equations in the “blow-up” area.