Passive scalars, moving boundaries, and Newton's law of cooling

Juhi Jang; Ian  Tice

doi:10.3934/dcds.2016.36.1383

Article Contents

2016, Volume 36, Issue 3: 1383-1413. Doi: 10.3934/dcds.2016.36.1383

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Passive scalars, moving boundaries, and Newton's law of cooling

Juhi Jang^1, and
Ian Tice^2,

1.
Department of Mathematics, University of California, Riverside, Riverside, CA 92521
2.
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213

Received: December 31, 2014

Revised: May 31, 2015

Published: May 2017

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Abstract

We study the evolution of passive scalars in both rigid and moving slab-like domains, in both horizontally periodic and infinite contexts. The scalar is required to satisfy Robin-type boundary conditions corresponding to Newton's law of cooling, which lead to nontrivial equilibrium configurations. We study the equilibration rate of the passive scalar in terms of the parameters in the boundary condition and the equilibration rates of the background velocity field and moving domain.

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Mathematics Subject Classification: Primary: 35Q35, 35B40, 35A23; Secondary: 35A23, 35Q30, 58J65.

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