Propagations Of Singularities In A Parabolic System With Coupled Nonlocal Sources

The main problems studied in this thesis are propagations of singularities in a parabolic system with coupled non-local nonlinear sources with exponent type, such as global existence, non-global existence, critical exponents and blow-up rate, etc. Besides we will introduce some linear algebraic systems containing all the nonlinear exponents in the systems to describe the critical exponents as well as the propagation of singularities of solutions for the reaction-diffusion systems considered.In the introduction, we give a discussion about the practical meaning and all kinds of background to the parabolic system. In Chapter 3, we firstly introduce the so called characteristic algebraic systems to describe the critical exponents for the parabolic system considered. We can get simple descriptions for the blow-up criteria by using the critical exponents. In Chapter 4, we will obtain the blow-up rate and the blow-up set estimate of the solutions for the problem considered. In Chapter 5, we will deal with the boundary layer profile of the reaction-diffusion system.