Convective Porous Medium Equations with Nonlinear Forcing at the Boundary

AbstractThis article deals with the global solutions and blow-up problems for the convective porous medium equationut=(um)xx+(μ/n)(un)x,x∈(0,1),t>0, with the nonlinear boundary conditions −(um)x(0,t)=aup(0,t), (um)x(1,t)=0, and positive initial datau(x,0)=u0(x)>0,x∈[0,1]. Here,m,n, μ,a, andpare all positive constants. Necessary and sufficient conditions for the global existence of all positive solutions are obtained