  In this paper, we prove global well-posedness of strong solutions to a class
of perturbed Camassa-Holm type equations in Besov spaces. It is shown that the
existence of global solutions depends only on the $L^1$-integrability of the
time-dependent parameters, but not on the shape or smoothness conditions on
initial data. As a by-product, we obtain a new global-in-time result for the
weakly dissipative Camassa-Holm type equations in Besov spaces, which
considerably improves the results in
\cite{wu2009global,wuyin2008blow,guo2009some}. Moreover, we derive two kinds of
precise blow-up criteria for a certain perturbed Camassa-Holm type equations in
Sobolev space, which in some sense tell us how the time-dependent parameters
affect the singularity formation of strong solutions.
