A class of nonlocal and degenerate quasilinear parabolic system not in divergence form Original Research Article

In this paper, we investigate the positive solution of the nonlocal and degenerate quasilinear parabolic system not in divergence form View the MathML sourceut=f(u)(Δu+a∫Ωvdx),vt=g(v)(Δv+b∫Ωudx) with null Dirichlet boundary conditions. The blow-up and global existence criteria are obtained. Furthermore, we prove that under certain conditions the solutions have global blow-up.