Blow-up in Nonlinear Heat Equations

Details Blow-up in Nonlinear Heat Equations Blow-up in Nonlinear Heat Equations

2006-09-06

arxiv.org/abs/math/0609161v2

Mathematics

Analysis of PDEs

41 pages

Scientific paper

We study the blow-up problem of one-dimensional nonlinear heat equations. Our result shows that for a certain class of initial conditions, the solutions blow up in finite time and we characterize the asymptotic dynamics of these solutions. The approach is analogous to one used in bifurcation theory and our techniques can be regarded as a time-dependent version of the Lyapunov-Schmidt decomposition.

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