RT Journal Article
T1 Blow-up with logarithmic nonlinearities
A1 Ferreira de Pablo, Raúl
A1 Pablo, Arturo de
A1 Rossi, Julio D.
AB We 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.
PB Elsevier
SN 0022-0396
YR 2007
FD 2007-09-01
LK https://hdl.handle.net/20.500.14352/49646
UL https://hdl.handle.net/20.500.14352/49646
LA eng
NO DGICYT
NO ANPC
DS Docta Complutense
RD 8 abr 2025