%0 Journal Article
%A Velázquez, J.J. L.
%A Galaktionov, V. A.
%A Posashkov, S. A.
%A Herrero, Miguel A.
%T On a general approach to extinction and blow-up for quasi-linear heat equations
%D 1993
%@ 0965-5425
%U https://hdl.handle.net/20.500.14352/57858
%X 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.
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