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A note on an ill-posed problem for the heat equation

Part of: Parabolic equations and systems

Published online by Cambridge University Press:  09 April 2009

Giorgio Talenti  and
Sergio Vessella
Giorgio Talenti
Affiliation:
Istituto Matematico, U. Dini viale Morgani 67/A, Firenze, Italy
Sergio Vessella
Affiliation:
Istituto Matematico, U. Dini viale Morgani 67/A, Firenze, Italy
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Abstract

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In this paper an ill-posed problem for the heat equation is investigated. Solutions u to the equation ut – uxx = 0, which are approximately known on the positive half-axis t = 0 and on some vertical lines x = x1,…, x = xn, are considered and stability estimates of these solutions are presented. We assume an a priori bound, governing the heat flow across the boundary x = 0.

MSC classification

Secondary: 35K05: Heat equation
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 3 , June 1982 , pp. 358 - 368
Copyright
Copyright © Australian Mathematical Society 1982

References

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