Propagation of Singularities of Nonlinear Heat Flow in Fissured Media

2011/03/30 by Andrey Shishkov, Shishkov, Andrey, Лаурент Верон +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1103.5893

openalex publication_date 2011/03/30 · openalex created_date 2022/11/15 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate the propagation of singularities in a nonlinear parabolic equation with strong absorption when the absorption potential is strongly degenerate following some curve in the (x,t) space. As a very simplified model, we assume that the heat conduction is constant but the absorption of the media depends stronly of the characteristic of the media. More precisely we suppose that the temperature u is governed by the following equation ∂_tu-Δu+h(x,t)u^p=0 inQ_T:=R^N× (0,T) where p>1 and h∈ C( Q_T). We suppose that h(x,t)>0 except when (x,t) belongs to some space-time curve.

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