Global existence and nonexistence for a class of degenerate parabolic systems (Q1411051)

The paper under review considers a nonlinear degenerate parabolic system \[ u_t= f_1(u) (\Delta u+ a_1 v),\qquad v_t= f_2(v) (\Delta v+ a_2 u). \] If \(f_1(u)= u^p\), \(f_2(v)= v^q\), \(p,q> 0\), above system is the one studied by M. X. Wang in his recent paper: some degenerate diffusion systems not in divergence form. The authors find out the necessary and sufficient condition for the global existence of the solution for above system under homogeneous Dirichlet boundary condition, thus Wang's results are extended.