RT Journal Article
T1 On a general approach to extinction and blow-up for quasi-linear heat equations
A1 Velázquez, J.J. L.
A1 Galaktionov, V. A.
A1 Posashkov, S. A.
A1 Herrero, Miguel A.
AB The authors study asymptotic behaviour of positive solutions of equations of the type ut =Δφ(u)±Q(u), where φ′ and Q are given positive functions. By determining an auxiliary function F(u) appearing in an expression posed by A. Friedman and B. McLeod, they obtain asymptotic estimates of solutions as t→T, blow-up or extinction time. These estimates have been established by other authors using different methods. Moreover, the paper poses a conjecture that, if the behaviour of u(0,t) as t→T near a blow-up or extinction point is known, all the information about the corresponding asymptotic expansions on small compact subsets near the origin is encoded in the first order ODE φ′(u)ur+rF(u)=0 for r>0 as t→T, where an optimal choice of F(u) is indicated in the paper.
PB Pergamon-Elsevier Science
SN 0965-5425
YR 1993
FD 1993
LK https://hdl.handle.net/20.500.14352/57858
UL https://hdl.handle.net/20.500.14352/57858
LA eng
DS Docta Complutense
RD 9 abr 2025