Abstract: We considered the blow-up properties of solutions to a class of fourth-order parabolic equations with Hessian terms by using the regularity theory of elliptic equations, Sobolev’s embedding inequalities and energy estimate methods. Firstly, we discussed the influence of weight functions and Hessian nonlinearity on the blow-up behavior of solutions.  Secondly, we  established differential inequalities for the square-integrable norms of the solutions, and qualitatively analyzed  several types of differential inequalities to give a lower bound estimate of the blow-up time and its qualitative relationship with the weight functions.

Key words: fourth-order parabolic equation, weight function, Hessian term, blow-up