Global existence and nonexistence for some degenerate and quasilinear parabolic systems (Q935135)

This paper concerns the degenerate and quasilinear parabolic system \[ u_t= u^\alpha v^\beta\Delta u+ au^pv^q, \] \[ v_t= u^\theta v^\eta\Delta v+ bu^r v^s \] with Dirichlet boundary conditions in a bounded domain \(\Omega\). The dependence of the global existence on the domain \(\Omega\) and on the number \[ (q-\beta)(r-\theta)- (\alpha+ 1- p)(\eta+ 1-s) \] is discussed.