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Approaching a vertex in a shrinking domain under a nonlinear flow

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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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
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
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