RT Book, Section
T1 Asymptotics near an extinction point for some semilinear heat equations
A1 Herrero, Miguel A.
A1 Velázquez, J.J. L.
A2 Chadam, John M.
A2 Rasmussen, Henning
AB We consider the Cauchy problem u t -u xx +u p =0,x∈ℝ,t>0,u(x,0)=u 0 (x),x∈ℝ, where 0<p<1, u 0 (x) is continuous, nonnegative, and bounded, with a single maximum at x=0 and such that u 0 (-x)=u 0 (x) for any x, lim x→∞ u 0 (x)=0. It is well known that the solution has some features which are absent in the superlinear case p≥1. For instance, there exists T>0 such that u(x,t)¬≡0 if t<T and u(x,t)≡0 for t≥T. Moreover, there exists a continuous curve ζ(t) such that lim t→T ζ(t)=0 and Ω + (t)={x: u(x,t)>0}={x: -ζ(t)<x<ζ(t)}. In this communication we describe some asymptotic results. Namely, lim t→T (T-t) 1 1-p u(ξ(T-t) 1/2 |ln(T-t)| 1/2 ,t)=(1-p) 1 1-p 1 - (1-p) 4p ξ 2 + 1 1-p uniformly on sets |ξ|≤C(T-t) 1/2 |ln(T-t)| 1/2 , and lim t→T ζ(t) (T-t) 1/2 |ln(T-t)|=4p 1-p 1/2 ·
PB Longman Scientific and Technical
SN 0-582-08768-6
YR 1993
FD 1993
LK https://hdl.handle.net/20.500.14352/60765
UL https://hdl.handle.net/20.500.14352/60765
NO Proceedings of the Fifth International Colloquium on Free Boundary Problems: Theory and Applications held in Montreal, Quebec, June 13–22, 1990
DS Docta Complutense
RD 4 abr 2025