Propagation of Singularities of Nonlinear Heat Flow in Fissured Media

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 \begin{equation}\label{I-1} \partial_{t}u-\Delta u+h(x,t)u^p=0\quad \text{in }Q_{T}:=R^N\times (0,T) \end{equation} where $p>1$ and $h\in C(\overline Q_{T})$. We suppose that $h(x,t)>0$ except when $(x,t)$ belongs to some space-time curve.
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https://hal.archives-ouvertes.fr/hal-00581042
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Submitted on : Wednesday, March 30, 2011 - 9:29:18 AM
Last modification on : Tuesday, August 13, 2019 - 2:00:02 PM
Long-term archiving on: Thursday, March 30, 2017 - 8:55:43 AM

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  • HAL Id : hal-00581042, version 1
  • ARXIV : 1103.5893

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Andrey Shishkov, Laurent Veron. Propagation of Singularities of Nonlinear Heat Flow in Fissured Media. 2011. ⟨hal-00581042⟩

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