Blow-up And Global Existence Of Solutions To Parabolic Equations With Variable Coefficients In A Multidimensional Bounded Domain

In this paper,we consider the global existence and blow-up phenomena for(?)respectively,when u(x,t)blow up,we estimate the upper and lower bounds of the blow-up time t*.In this paper,? is a bounded region with smooth boundary,particularly,we need ? to be star-shaped region in the proof of the global existence of the solution and the lower bound estimation of the blow up time t*.When we estimate the lower bound of t*,we used a lemma which has a wide application and we generalize it from three-dimensions to N-dimensions.