Two-point boundary value problems for linear evolution equations

A. S. Fokas, Beatrice Pelloni

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


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 andqt + qxxx = 0.
Original languageEnglish
Pages (from-to)521-543
Number of pages23
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number3
Publication statusPublished - Nov 2001


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