TY - JOUR
T1 - Well-posed boundary value problems for linear evolution equations on a finite interval
AU - Pelloni, Beatrice
PY - 2004/3
Y1 - 2004/3
N2 - We identify the class of smooth boundary conditions that yield an initial-boundaryvalue problem admitting a unique smooth solution for the case of a dispersive linearevolution PDE of arbitrary order, in one spatial dimension, defined on a finiteinterval.This result is obtained by an application of a spectral transform method, introducedby Fokas, which allows us to reduce the problem to the study of the singularitiesof the set of functions arising as the unique solution of a certain linearsystem.
AB - We identify the class of smooth boundary conditions that yield an initial-boundaryvalue problem admitting a unique smooth solution for the case of a dispersive linearevolution PDE of arbitrary order, in one spatial dimension, defined on a finiteinterval.This result is obtained by an application of a spectral transform method, introducedby Fokas, which allows us to reduce the problem to the study of the singularitiesof the set of functions arising as the unique solution of a certain linearsystem.
UR - https://www.scopus.com/pages/publications/1642602556
U2 - 10.1017/S0305004103007205
DO - 10.1017/S0305004103007205
M3 - Article
SN - 0305-0041
VL - 136
SP - 361
EP - 382
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
IS - 2
ER -