Herrero, Miguel A.Velázquez, J.J. L.Ni, Wei-MingPeletier, L. A.Vázquez, Juan Luis2023-06-202023-06-2019930-387-94068-510.1007/978-1-4612-0885-3_7https://hdl.handle.net/20.500.14352/60763Proceedings of the IMA Workshop held at the University of Minnesota, Minneapolis, Minnesota, May 13–18, 1991The 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.engbook parthttp://link.springer.com/chapter/10.1007%2F978-1-4612-0885-3_7http://www.springer.comopen access517.956.4Semilinear parabolic problemsblow upasymptotic behaviour of solutionsEcuaciones diferenciales1202.07 Ecuaciones en Diferencias