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March/April 2015 Spatial behavior in phase-lag heat conduction
Ramón Quintanilla, Reinhard Racke
Differential Integral Equations 28(3/4): 291-308 (March/April 2015).

Abstract

In this paper, we study the spatial behavior of solutions to the equations obtained by taking formal Taylor approximations to the heat conduction dual-phase-lag and three-phase-lag theories, reflecting Saint-Venant's principle. Depending on the relative order of derivation, with respect to the time, we propose different arguments. One is inspired by the arguments for parabolic problems and the other is inspired by the arguments for hyperbolic problems. In the first case, we obtain a Phragmén-Lindelöf alternative for the solutions. In the second case, we obtain an estimate for the decay as well as a domain of influence result. The main tool to manage these problems is the use of an exponentially weighted Poincaré inequality.

Citation

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Ramón Quintanilla. Reinhard Racke. "Spatial behavior in phase-lag heat conduction." Differential Integral Equations 28 (3/4) 291 - 308, March/April 2015.

Information

Published: March/April 2015
First available in Project Euclid: 4 February 2015

zbMATH: 1363.35236
MathSciNet: MR3306564

Subjects:
Primary: 35L35, 80A20

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.28 • No. 3/4 • March/April 2015
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