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Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 11
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Articles

Spatial behavior for solutions in heat conduction with two delays

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Pages 2331-2341 | Received 11 Jul 2014, Accepted 30 Oct 2014, Published online: 21 Nov 2014
 

Abstract

In this note, we investigate the spatial behavior of the solutions of the equation proposed to describe a theory for the heat conduction with two delay terms. We obtain an alternative of the Phragmén-Lindelöf type, which means that the solutions either decay or blow-up at infinity, both options in an exponential way. We also describe how to obtain an upper bound for the amplitude term. This is the first contribution on spatial behavior for partial differential equations involving two delay terms. We use energy arguments. The main point of the contribution is the use of an exponentially weighted energy function.

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Acknowledgements

The authors thank to the anonymous referees their useful comments. This work is supported by the project “Análisis Matemático de las Ecuaciones en Derivadas Parciales de la Termomecánica” (MTM2013-42004-P) of the Spanish Ministry of Economy and Competitiveness.

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