Well-posed two-point initial-boundary value problems with arbitrary boundary conditions
Smith, D. A. (2012) Well-posed two-point initial-boundary value problems with arbitrary boundary conditions. Mathematical Proceedings of the Cambridge Philosophical Society, 152 (3). pp. 473-496. ISSN 1469-8064
To link to this article DOI: 10.1017/S030500411100082X
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.