TY - CHAP
T1 - The Role of Periodicity in the Solution of Third Order Boundary Value Problems
AU - Pelloni, Beatrice
AU - Smith, David
N1 - Funding Information:
The authors thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during programme Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves, when work on this paper was undertaken. This work was supported by EPSRC Grant Number EP/R014604/1.
Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.
PY - 2023/9/22
Y1 - 2023/9/22
N2 - In this short paper, we elucidate how the solution of certain illustrative boundary value problems for the Airy equation 푢푡+푢푥푥푥=0 on [0, 1] can be expressed as a perturbation of the solution of the purely periodic problem. The motivation is to understand the role boundary conditions play in the properties of the solution. This is particularly important in related work on the solution of linear dispersive problems with discontinuous initial data and the phenomena of revivals and fractalization.
AB - In this short paper, we elucidate how the solution of certain illustrative boundary value problems for the Airy equation 푢푡+푢푥푥푥=0 on [0, 1] can be expressed as a perturbation of the solution of the purely periodic problem. The motivation is to understand the role boundary conditions play in the properties of the solution. This is particularly important in related work on the solution of linear dispersive problems with discontinuous initial data and the phenomena of revivals and fractalization.
KW - Fokas transform method
KW - Initial boundary value problems
KW - Regularity of solutions
KW - Revivals and fractalization
UR - http://www.scopus.com/inward/record.url?scp=85174491856&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-37404-3_23
DO - 10.1007/978-3-031-37404-3_23
M3 - Chapter (peer-reviewed)
SN - 9783031374036
SN - 9783031374067
T3 - Springer Proceedings in Complexity
SP - 333
EP - 345
BT - Chaos, Fractals and Complexity
A2 - Bountis, Tassos
A2 - Vallianatos, Filippos
A2 - Provata, Astero
A2 - Kugiumtzis, Dimitris
A2 - Kominis, Yannis
PB - Springer
ER -