TY - JOUR

T1 - Interaction between degenerate diffusion and shape of domain

AU - Magnanini, R.

AU - Sakaguchi, S.

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2007

Y1 - 2007

N2 - We consider the flow of a gas into a bounded tank Ω with smooth boundary∂ Ω. Initially Ω is empty, and at all times the density of the gas is kept constant on ∂ Ω. Choose a number R > 0 sufficiently small that, for any point x in Ω having distance R from ∂ Ω, the closed ball B with radius R centred at x intersects ∂ Ω at only one point. We show that if the gas content of such balls B is constant at each given time, then the tank Ω must be a ball. In order to prove this, we derive an asymptotic estimate for gas content for short times. Similar estimates are also derived in the case of the evolution p-Laplace equation for p ≥2.

AB - We consider the flow of a gas into a bounded tank Ω with smooth boundary∂ Ω. Initially Ω is empty, and at all times the density of the gas is kept constant on ∂ Ω. Choose a number R > 0 sufficiently small that, for any point x in Ω having distance R from ∂ Ω, the closed ball B with radius R centred at x intersects ∂ Ω at only one point. We show that if the gas content of such balls B is constant at each given time, then the tank Ω must be a ball. In order to prove this, we derive an asymptotic estimate for gas content for short times. Similar estimates are also derived in the case of the evolution p-Laplace equation for p ≥2.

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U2 - 10.1017/S0308210505001071

DO - 10.1017/S0308210505001071

M3 - Article

AN - SCOPUS:34249014032

VL - 137

SP - 373

EP - 388

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 2

ER -