Herrero García, Miguel ÁngelLópez Velázquez, Juan José2023-06-202023-06-201992Herrero, M. A., y J. J. L. Velázquez. «Blow–Up Profiles in One–Dimensional. Semilinear Parabolic Problems». Communications in Partial Differential Equations, vol. 17, n.o 1-2, enero de 1992, pp. 205-19. DOI.org (Crossref), https://doi.org/10.1080/03605309208820839.0360-530210.1080/03605309208820839https://hdl.handle.net/20.500.14352/57863Let u be a solution of the Cauchy problem ut=uxx+up, x∈R, t>0, u(x,0)=u0(x), x∈R, where p>1 and u0 is continuous, nonnegative, and bounded. Suppose that u blows up at t=T<∞ and u(x,t)≢(p−1)−1/(p−1)(T−t)−1/(p−1). The authors show that the blow-up set is discrete. Also, if x=0 is a blow-up point then either limx→0[|x|2/log|x|]1/(p−1)u(x,T)=[8p/(p−1)2] 1/(p−1) or there exists a constant C>0 and an even integer m≥4 such that limx→0|x|m/(p−1)u(x,T)=C.journal articlehttp://www.doi.org/10.1080/03605309208820839http://www.tandfonline.commetadata only access517.9517.956.4Heat-equationsCauchy problemEcuaciones diferenciales1202.07 Ecuaciones en Diferencias