BLOW-UP FOR PARABOLIC EQUATIONS IN NONLINEAR DIVERGENCE FORM WITH TIME-DEPENDENT COEFFICIENTS.

In this article, we study the blow-up of solutions to the nonlinear parabolic equation in divergence form, ... where Ω is a bounded convex domain in Rn (n ≥ 2) with smooth boundary Ω. By constructing suitable auxiliary functions and using a differential inequality technique, when Ω ⊂ Rn (n ≥ 2), we establish conditions for the solution blow up at a finite time, and conditions for the solution to exist for all time. Also, we find an upper bound for the blow-up time. In addition, when Ω ⊂ Rn with (n ≥ 3), we use a Sobolev inequality to obtain a lower bound for the blow-up time. [ABSTRACT FROM AUTHOR]