Blow-up issues for the weakly dissipative periodic b-family of equations revisited

Abstract

In this paper, we study the weakly dissipative asymptotically equivalent shallow water wave equations on the circle, which is called the weakly dissipative periodic b-family of equations. Under the effect of dissipation, we derive two blow-up criteria to this equation with certain initial data. When the parameters α, λ, and b belong to a suitable range, our present blow-up criteria improve and extend the previous relevant blow-up results.