Universality in Blow-Up for Nonlinear Heat Equations

Details Universality in Blow-Up for Nonlinear Heat Equations Universality in Blow-Up for Nonlinear Heat Equations

1993-06-21

arxiv.org/abs/chao-dyn/9306007v1

Physics

Condensed Matter

38 pages

Scientific paper

10.1088/0951-7715/7/2/011

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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