The Quenching Problem in the Nonlinear Heat Equations

Details The Quenching Problem in the Nonlinear Heat Equations The Quenching Problem in the Nonlinear Heat Equations

2006-12-05

arxiv.org/abs/math/0612110v2

Mathematics

Analysis of PDEs

33 Pages

Scientific paper

In this paper we study the quenching problem in nonlinear heat equations with
power nonlinearities. For nonlinearities of power p<0 and for an open set of
slowly varying initial conditions we prove that the solutions will collapse in
a finite time. We find the collapse profile and estimate the remainder.

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