A class of fourth-order parabolic systems with time dependent coefficients with blow-up solutions

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. 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 & lowast;, deriving an upper bound for t & lowast;. Moreover, by introducing suitable conditions on the source terms, we obtain a lifespan of the solution, i.e. a time interval [0, T], where the solution exists and remains bounded, by deriving a lower bound T of the blow-up time t & lowast;.