Convective porous medium equations with nonlinear forcing at the boundary

[摘要] This article deals with the global solutions and blow-up problems for the convective porous medium equation u(t) = (u(m))(xx) + (mu/n)(u(n))(x), x is an element of (0, 1), t > 0, with the nonlinear boundary conditions - (u(m))(x)(0, t) = au(p)(0, t), (u(m)),(1, t) = 0, and positive initial data u(x,0) = u(0)(x) > 0, x is an element of [0, 1]. Here, m, n, mu, a, and p are all positive constants. Necessary and sufficient conditions for the global existence of all positive solutions are obtained. (C) 1997 Academic Press.

[发布日期] 1997-07-01