RT Book, Section
T1 Some results on blow up for semilinear parabolic problems
A1 Herrero, Miguel A.
A1 Velázquez, J.J. L.
A2 Ni, Wei-Ming
A2 Peletier, L. A.
A2 Vázquez, Juan Luis
AB The authors describe the asymptotic behavior of blow-up for the semilinear heat equation ut=uxx+f(u) in R×(0,T), with initial data u0(x)>0 in R, where f(u)=up, p>1, or f(u)=eu. A complete description of the types of blow-up patterns and of the corresponding blow-up final-time profiles is given. In the rescaled variables, both are governed by the structure of the Hermite polynomials H2m(y). The H2-behavior is shown to be stable and generic. The existence of H4-behavior is proved. A nontrivial blow-up pattern with a blow-up set of nonzero measure is constructed. Similar results for the absorption equation ut=uxx−up, 0<p<1, are discussed.
PB Springer
SN 0-387-94068-5
YR 1993
FD 1993
LK https://hdl.handle.net/20.500.14352/60763
UL https://hdl.handle.net/20.500.14352/60763
LA eng
NO Proceedings of the IMA Workshop held at the University of Minnesota, Minneapolis, Minnesota, May 13–18, 1991
DS Docta Complutense
RD 6 abr 2025