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Initial-boundary value problems for linear PDEs with variable coefficients

Published online by Cambridge University Press:  01 July 2007

P. A. TREHARNE  and
A. S. FOKAS
P. A. TREHARNE
Affiliation:
School of Mathematics and Statistics, University of Sydney, Sydney 2006, Australia. e-mail: P.Treharne@maths.usyd.edu.au
A. S. FOKAS
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA. e-mail: T.Fokas@damtp.cam.ac.uk
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Abstract

A new approach for studying initial-boundary value problems for linear partial differential equations (PDEs) with variable coefficients was introduced recently by the second author, and was applied to PDEs involving second order derivatives. Here, we extend this approach further to solve an initial-boundary value problem for a third-order evolution PDE with a space-dependent coefficient. The analysis is presented in such a way that it can be applied to PDEs with higher derivatives, and thus provides a method for solving initial-boundary value problems for a certain class of linear evolution equations with variable coefficients of arbitrary order.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 1 , July 2007 , pp. 221 - 242
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

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