A Nonlocal Reaction Diffusion Equations

In this article,we study a class of nonlocal reaction diffusion systems that arisein the theory of ignition.In the frist chapter of this article,we consider the Cauchyproblem. We obtain the local existence and uniqueness for the problem and give theexistence of the global solutions and the finite time blow-up result. In the secondChapter of the article,we consider the Neumann boundary condition.We prove thelocal solvabiity of the problem by sChauder fixed point theorem. We establish theexistence of global solutions and also the blow-up result.