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arxiv: chao-dyn/9306007 · v1 · submitted 1993-06-21 · chao-dyn · cond-mat· nlin.CD

Universality in Blow-Up for Nonlinear Heat Equations

J.Bricmont (UCL , Physique Theorique , Louvain-la-Neuve , Belgium) , A.Kupiainen (Helsinki University , Mathematics Department , Helsinki , Finland) This is my paper
classification chao-dyn cond-matnlin.CD
keywords blow-upheatnonlinearsolutionsaccordingaroundblowing-upclassical
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We consider the classical problem of the blowing-up of solutions of the nonlinear heat equation. We show that there exist infinitely many profiles around the blow-up point, and for each integer $k$, we construct a set of codimension $2k$ in the space of initial data giving rise to solutions that blow-up according to the given profile.

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