| Sumario: | We study nonnegative solutions of {ut = (um)xx, (x,t)ε(0,L) × (0,T), {-(um)x(0,t) = up(0,t), tε(0,T), {(u,m)x(L,t) = -λuq(L,t), tε(0,T), {u(x,0) = u0(x), xε(0,L), where m, p, q, λ and L are positive parameters. For different values of the parameters three situations may occur: (1) all solutions of this problem exist for all t > 0; (2) for certain initial data functions the solution exists for all t > 0 while for others the solution blows up as t ↗ T for some finite T; (3) excepting the trivial solution when u0 ≡ 0, all solutions blow up as t ↗ T for some finite T. We identify in terms of the parameters which of them actually happens. For solutions which blow up we find the blow-up rate and the blow-up set. © 2002 Elsevier Science (USA).
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