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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  and
B. PELLONI
A. S. FOKAS
Affiliation:
Department of Mathematics, Imperial College, London SW7 2BZ. e-mail: [email protected], [email protected]
B. PELLONI
Affiliation:
Department of Mathematics, Imperial College, London SW7 2BZ. e-mail: [email protected], [email protected] Current address: Department of Mathematics, University of Reading, Reading RG6 6AX, UK.
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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
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 131 , Issue 3 , November 2001 , pp. 521 - 543
Copyright
© 2001 Cambridge Philosophical Society

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