The Global Existence And Blow-up Of Solutions For A Certain Parabolic System

In this paper, we consider the following semilinear parabolic system: (1)where,,,,.and,are continuous We discuss the global existence and blow-up of solutions of the system (1), using the method applied to the reference [1], and work out its critical exponents. We obtain the following resultsTheorem 1 When,and0,,if , the solutions for the system (1) blow up in finite time.Theorem 2 When ,if are large enough, the solutions for the system (1) blow up in finite time;if are small enough, the global solutions for the system (1) exist.Where , ,andare the solutions of the following equations:.In the forth part of this paper, we will extend former results to the case of .We also deal with a certain multidimension, degenerated and singular semilinear parabolic system with nonlocal source,and prove that its solutions would blow up in finite time under appropriate hypothesis.