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Two-point boundary value problems for linear evolution equations

Fokas, A. S. and Pelloni, B. (2001) Two-point boundary value problems for linear evolution equations. Mathematical Proceedings of the Cambridge Philosophical Society, 131 (3). pp. 521-543. ISSN 1469-8064

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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 nite 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.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:15684
Additional Information:DOI 10.1017/S0305004101005436 not working
Publisher:Cambridge University Press


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