A class of nonlocal and degenerate quasilinear parabolic system not indivergence form

摘要

In this paper, we investigate the positive solution of the nonlocal and degeneratequasilinear parabolic system not in divergence form u_t= f(u) (Δu+a∫_Ω vdx),v_t= g(v) (Δv+b∫_Ω udx)with null Dirichlet boundary conditions. The blow-up and global existence criteria are obtained. Furthermore, we prove that under certain conditions the solutions have globalblow-up.