Differential and Integral Equations

Spatial behavior in phase-lag heat conduction

Ramón Quintanilla and Reinhard Racke

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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.

Article information

Differential Integral Equations, Volume 28, Number 3/4 (2015), 291-308.

First available in Project Euclid: 4 February 2015

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L35: Initial-boundary value problems for higher-order hyperbolic equations 80A20: Heat and mass transfer, heat flow


Quintanilla, Ramón; Racke, Reinhard. Spatial behavior in phase-lag heat conduction. Differential Integral Equations 28 (2015), no. 3/4, 291--308. https://projecteuclid.org/euclid.die/1423055229

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