退化反应扩散方程组解的整体存在和有限爆破

摘要

The properties of solutions for a degenerate reaction-diffusion system ut =v p 1 Δu +a∫Ωu m1 vq 1 dx ( ) ,vt = u p 2 Δv +b∫Ωv m2 uq2 dx ( ) with null Dirichlet boundary conditions and nonlocal sources are investigated.The sufficient conditions for the global existence and the finite time blow-up of solution to the system are established by comparison theorem and upper-lower solution method.It can clearly understand the global existence,the relationship between the initial value,the blow-up of solution and the direct relation of the area size.%研究了一类具有齐次 Dirichlet 边界条件和带有非局部反应项的退化抛物方程组 ut =v p 1Δu +a∫Ωu m1 vq 1 dx (),vt = u p 2Δv +b∫Ωv m2 uq2 dx ()解的性质,通过比较原理和上下解方法得到解整体存在和有限爆破的充分条件,明确了解的整体存在性与初始值的关系,以及解的爆破性和区域大小的直接关系。