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Initial and relative limiting behaviour of temperatures on a strip

Part of: Representations of solutions Classical measure theory Partial differential equations Parabolic equations and systems

Published online by Cambridge University Press:  09 April 2009

N. A. Watson
N. A. Watson
Affiliation:
Department of Mathematics University of CanterburyChristchurch, New Zealand
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Abstract

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Let u be a solution of the heat equation which can be written as the difference of two non-negative solutions, and let v be a non-negative solution. A study is made of the behaviour of u(x, t)/v(x, t) as t → 0+. The methods are based on the Gauss-Weierstrass integral representation of solutions on Rn × ]0, a[ and results on the relative differentiation of measures, which are employed in a novel way to obtain several domination, non-negativity, uniqueness and representation theorems.

MSC classification

Secondary: 35K05: Heat equation 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35C15: Integral representations of solutions 28A15: Abstract differentiation theory, differentiation of set functions

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 2 , October 1982 , pp. 213 - 228
Copyright
Copyright © Australian Mathematical Society 1982

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