Comportement générique au voisinage d'un point d'explosion pour des solutions d'équations paraboliques unidimensionnelles

Abstract

We consider the Cauchy problem (1) ut=uxx+up, x∈R, t>0, p>1, (2) u(x,0)=u0(x),x∈R, where u0(x) is continuous, nonnegative and bounded. Assume that the solution u(x,t) of (1), (2) blows up at x=0, t=T. We describe here the generic asymptotic behaviour of u(x,t) as (x,t) approaches (0,T)