Nonlinear Degenerate Parabolic System With Weighted Non-local Source

In this paper, we study positive solutions of the nonlinear degenerate system with weighted nonlocal source u_t= f(u)(Δu+a(x)∫_Ωv~p(x,t)dx),v_t = g(v)(Δv+b(x)∫_Ωu~q(x, t)dx), subject to homogeneous Dirichlet boundary condition. We obtain that the solutions are global if 0 < p, q < 1, and may be both global and non-global when p, q≥1, depending on the weight functions a(x), b(x).In the introduction, we give the background to the nonlocal source parabolic equation. In Chapter 2, we give some basic knowledge to be used in this paper. In Chapter 3, we describe the main results of the paper, and then prove the theorems in Chapter 4. In the last chapter, we discuss all the conclusions obtained in this paper.