The maximum time of existence of solutions for the evolution problem

Abstract

The aim of this research is to study Maximum time of existence of solution (life span) to some evolution problems. In order to obtain a lower bound estimate of life span of solution, we invistigated the local existence of our problems. Furthermore, to give the upper bound estimate of life span of the blowing up solution, we studied the global non existence, the estimate of the life span of the blow-up of solutions, and both the local and global existence of solutions, in addition to both the lower and upper bound estimates of the life span all together. This research is based on the test function and energy methods ..