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Two-point boundary value problems for linear evolution equations

Published online by Cambridge University Press:  26 November 2001

A. S. FOKAS
Affiliation:
Department of Mathematics, Imperial College, London SW7 2BZ. e-mail: a.fokas@damtp.cam.ac.uk, b.pelloni@ic.ac.uk
B. PELLONI
Affiliation:
Department of Mathematics, Imperial College, London SW7 2BZ. e-mail: a.fokas@damtp.cam.ac.uk, b.pelloni@ic.ac.uk Current address: Department of Mathematics, University of Reading, Reading RG6 6AX, UK.

Abstract

We study boundary value problems for a linear evolution equation with spatial derivatives of arbitrary order, on the domain 0 < x < L, 0 < t < T, with L and T positive finite constants. We present a general method for identifying well-posed problems, as well as for constructing an explicit representation of the solution of such problems. This representation has explicit x and t dependence, and it consists of an integral in the k-complex plane and of a discrete sum. As illustrative examples we solve some two-point boundary value problems for the equations iqt + qxx = 0 and qt + qxxx = 0.

Type
Research Article
Copyright
© 2001 Cambridge Philosophical Society

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