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Diffusivity determination in nonlinear diffusion

Published online by Cambridge University Press:  16 July 2009

Carmen Cortázar ,
Manuel Elgueta  and
Juan Luis Vázquez
Carmen Cortázar
Affiliation:
Departamento de Matemática, Pontificia Universidad Católica, Casilla 6177, Santiago de Chile, Chile
Manuel Elgueta
Affiliation:
Departamento de Matemática, Pontificia Universidad Católica, Casilla 6177, Santiago de Chile, Chile
Juan Luis Vázquez
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049, Madrid, Spain
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Abstract

We are concerned with the problem of determining the diffusivity D of a diffusion process governed by the equation ut = (Dux)x', under the assumption that D depends on u. The main point consists in the observation that there exist solutions of travelling-wave type and that the dependence D = D(u) can be explicitly found in terms of the profile of such solutions. The property of finite propagation speed is required for this method to work. We propose two concrete implementations of the inverse problem, and give a rigorous mathematical proof of our statements. We also describe the application of the travelling-wave method to another interesting class of nonlinear parabolic equations.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 2 , Issue 2 , June 1991 , pp. 159 - 169
Copyright
Copyright © Cambridge University Press 1991

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