Global existence and nonexistence for a strongly coupled parabolic system with nonlinear boundary conditions (Q2505380)

The authors study the following system \(u_t=v^m\Delta u,v_t=u^n\Delta v\) over a bounded domain, coupled with the nonlinear boundary conditions \(\partial u/\partial\eta=u^\alpha v^p, \partial v/\partial\eta=u^qv^\beta.\) They prove that the above system admits a global positive solution only if \(\alpha<1,\beta<1\) and \((m+p)(n+q)\leq (1-\alpha)(1-\beta).\)