Continuity of the quenching time in a semilinear parabolic equation

Théodore Boni; Firmin N'Gohisse

Annales UMCS, Mathematica (2008)

  • Volume: 62, Issue: 1, page 37-48
  • ISSN: 2083-7402

Abstract

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In this paper, we consider the following initial-boundary value problem [...] where Ω is a bounded domain in RN with smooth boundary ∂Ω, p > 0, Δ is the Laplacian, v is the exterior normal unit vector on ∂Ω. Under some assumptions, we show that the solution of the above problem quenches in a finite time and estimate its quenching time. We also prove the continuity of the quenching time as a function of the initial data u0. Finally, we give some numerical results to illustrate our analysis.

How to cite

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Théodore Boni, and Firmin N'Gohisse. "Continuity of the quenching time in a semilinear parabolic equation." Annales UMCS, Mathematica 62.1 (2008): 37-48. <http://eudml.org/doc/267695>.

@article{ThéodoreBoni2008,
abstract = {In this paper, we consider the following initial-boundary value problem [...] where Ω is a bounded domain in RN with smooth boundary ∂Ω, p > 0, Δ is the Laplacian, v is the exterior normal unit vector on ∂Ω. Under some assumptions, we show that the solution of the above problem quenches in a finite time and estimate its quenching time. We also prove the continuity of the quenching time as a function of the initial data u0. Finally, we give some numerical results to illustrate our analysis.},
author = {Théodore Boni, Firmin N'Gohisse},
journal = {Annales UMCS, Mathematica},
keywords = {Quenching; nonlinear parabolic equation; numerical quenching time; quenching; dependence on initial data},
language = {eng},
number = {1},
pages = {37-48},
title = {Continuity of the quenching time in a semilinear parabolic equation},
url = {http://eudml.org/doc/267695},
volume = {62},
year = {2008},
}

TY - JOUR
AU - Théodore Boni
AU - Firmin N'Gohisse
TI - Continuity of the quenching time in a semilinear parabolic equation
JO - Annales UMCS, Mathematica
PY - 2008
VL - 62
IS - 1
SP - 37
EP - 48
AB - In this paper, we consider the following initial-boundary value problem [...] where Ω is a bounded domain in RN with smooth boundary ∂Ω, p > 0, Δ is the Laplacian, v is the exterior normal unit vector on ∂Ω. Under some assumptions, we show that the solution of the above problem quenches in a finite time and estimate its quenching time. We also prove the continuity of the quenching time as a function of the initial data u0. Finally, we give some numerical results to illustrate our analysis.
LA - eng
KW - Quenching; nonlinear parabolic equation; numerical quenching time; quenching; dependence on initial data
UR - http://eudml.org/doc/267695
ER -

References

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