Well-posedness and conditioning of 3rd and higher order two-point initial-boundary value problems

Abstract

We discuss initial-boundary value problems of arbitrary spatial order subject to arbitrary boundary conditions. We formalise the concept of the conditioning of such a problem and show that it represents a necessary criterion for well-posedness. The other requirement for well-posedness, the convergence of certain series, is also analysed. We illustrate these results with a full classification of 3rd order problems having non-Robin boundary conditions. Part of this work is devoted to correcting an oversight in the author's earlier work Well-posed two-point initial-boundary value problems with arbitrary boundary conditions in volume 152 of Math. Proc. Camb. Philos. Soc.