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Title: Spectral theory of ordinary and partial linear differential operators on finite intervals
Author: Smith, D. A.
ISNI:       0000 0004 2721 2409
Awarding Body: University of Reading
Current Institution: University of Reading
Date of Award: 2011
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A new, unified transform method for boundary value problems on linear and integrable nonlinear partial differential equations was recently introduced by Fokas. We consider initial- boundary value problems for linear, constant-coefficient evolution equations of arbitrary order on a finite domain. We use Fokas' method to fully characterise well-posed problems. For odd order problems with non-Robin boundary conditions we identify sufficient conditions that may be checked using a simple combinatorial argument without the need for any analysis. We derive similar conditions for the existence of a series representation for the solution to a well-posed problem. We also discuss the spectral theory of the associated linear two-point ordinary differential operator. We give new conditions for the eigenfunctions to form a complete system, characterised in terms of initial-boundary value problems.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available