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

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