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Herrero, Miguel A. and Ughi, M. and Velázquez, J.J. L.
(2004)
*Approaching a vertex in a shrinking domain under a nonlinear flow.*
NoDea-Nonlinear Differential Equations and Applications, 11
.
pp. 1-28.
ISSN 1021-9722

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Official URL: http://www.springerlink.com/content/2kyc4v8wknhrn1da/fulltext.pdf

## Abstract

We consider here the homogeneous Dirichlet problem for the equation u(t)= uΔu - γ|∇u|(2) with γ ∈ R, u ≥ 0, in a noncylindrical domain in space-time given by |x| ≤ R(t) = (T - t)(p), with p > 0. By means of matched asymptotic expansion techniques we describe the asymptotics of the maximal solution approaching the vertex x = 0, t = T, in the three different cases p > 1/2, p = 1/2(vertex regular), p < 1/2 (vertex irregular).

Item Type: | Article |
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Uncontrolled Keywords: | Asymptotics; nonlinear flow; degenerate parabolic equation; viscosity solutions; Dirichlet problem; heat-equation; singularities; regularity; points |

Subjects: | Sciences > Physics > Mathematical physics Sciences > Mathematics > Differential equations |

ID Code: | 16426 |

Deposited On: | 19 Sep 2012 08:16 |

Last Modified: | 12 Dec 2018 15:07 |

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