Well-posed two-point initial-boundary value problems with arbitrary boundary conditions

Details Well-posed two-point initial-boundary value problems with arbitrary boundary conditions Well-posed two-point initial-boundary value problems with arbitrary boundary conditions

2011-04-29

arxiv.org/abs/1104.5571v2

Mathematics

Analysis of PDEs

21 pages

Scientific paper

We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the boundary conditions that specify well-posed problems using Fokas' transform method. We also give a sufficient condition guaranteeing that the solution can be represented using a series. The relevant condition, the analyticity at infinity of certain meromorphic functions within particular sectors, is significantly more concrete and easier to test than the previous criterion, based on the existence of admissible functions.

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