Behaviour in time of solutions to fourth-order parabolic systems with time dependent coefficients

This paper deals with a class of initial-boundary value problems for nonlinear fourth order parabolic systems with time dependent coefficients in a bounded domain $\mathrm{\Omega }\subset {\mathbb{R}}^N,N\ge 2$. Introducing suitable conditions on the source terms, we obtain a time interval $[0,T],$ where the solution remains bounded by deriving a lower bound $T$ of $t^{\ast }$. Moreover, we establish conditions on the shape of the spatial domain and on data sufficient to guarantee that the solution blows up in finite time $t^{\ast }$, deriving an upper bound for $t^{\ast }$.