Ferreira de Pablo, RaúlPablo, Arturo deRossi, Julio D.2023-06-202023-06-202007-09-010022-039610.1016/j.jde.2007.05.004https://hdl.handle.net/20.500.14352/49646We study the asymptotic behaviour of nonnegative solutions of the nonlinear diffusion equation in the half-line with a nonlinear boundary condition, ut = uxx − _(u + 1) logp(u + 1) (x, t) € R+ × (0, T),−ux(0, t) = (u + 1) logq(u + 1)(0, t) t € (0, T),u(x, 0) = u0(x) x € R+, with p, q, _ > 0. We describe in terms of p, q and when the solution is global in time and when it blows up in finite time. For blow-up solutions we find the blow-up rate and the blow-up set and we describe the asymptotic behaviour close to the blow-up time, showing that a phenomenon of asymptotic simplification takes place. We finally study the appearance of extinction in finite time.engjournal articleopen access517.9Blow-upAsymptotic behaviourNonlinear boundary conditionsEcuaciones diferenciales1202.07 Ecuaciones en Diferencias