Phragmen-Lindelof and continuous dependence type results in generalized dissipative heat conduction

Jong Chul Song; Dall Sun Yoon

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 1998; 35(4): 945-960

Printed December 1, 1998

Phragmen-Lindelof and continuous dependence type results in generalized dissipative heat conduction

Jong Chul Song and Dall Sun Yoon

Hanyang University and Hanyang University

Abstract

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Abstract

This paper is concerned with investigating the asymptotic behavior of end effects for a generalized heat conduction problem with an added dissipation term defined on a three-dimensional semi-infinite cylinder. With homogeneous Dirichlet conditions on the lateral surface of the cylinder it is shown that solutions either grow exponentially or decay exponentially in the distance from the finite end of the cylinder. In particular, to render decay estimate explicit, we pattern after the analysis of Payne and Song \cite{PSzamp, PShutter}. The continuous dependence effect of perturbing the equations parameters is also investigated.

Keywords: heat conduction, continuous dependence, decay estimate

MSC numbers: 35K50, 35B20, 35B30, 35B40