A Nonlinear Diffusion Equation With Weighted Nonlocal Source

In this paper, we study positive solutions of the nonlinear degenerate equation withweighted nonlocal source u_t=f(u)(Δu+a(x)f_Ωu~p(x,t)dx) subject to homogeneousDirichlet boundary condition. We obtain that the solutions are global if 0＜p＜1, andmay be both global and non-global when p≥1, depending on the weight function a(x).In addition, the blow-up rate is determined.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, wedescribe the main results of the paper, and then prove the theorems in Chapter 4. In thelast chapter, we discuss all the conclusions obtained in this paper.