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 andqt + qxxx = 0.
| Original language | English |
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| Pages (from-to) | 521-543 |
| Number of pages | 23 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Volume | 131 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Nov 2001 |