Convective Porous Medium Equations with Nonlinear Forcing at the Boundary*

This article deals with the global solutions and blow-up problems for the convective porous medium equation uts um.x xq mrn. un.x , xg 0, 1., t)0, with the nonlinear boundary conditions y um.x 0, t.sau p 0, t., um.x 1, t.s0, and positive initial data u x, 0.su0 x.)0, xgw0, 1x. Here, m, n, m, a, and p are all positive constants. Necessary and sufficient conditions for the global existence of all positive solutions are obtained.