A transform method for linear evolution PDEs on a finite interval

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 70, Issue 4, 2005, Pages 564-587

  Fokas, A S ^a   Pelloni, B ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF READING   (United Kingdom)

Author keywords

Boundary value problems; Evolution PDEs; Generalized Fourier transforms; Spectal transforms

Indexed keywords

BOUNDARY CONDITIONS; FOURIER TRANSFORMS; INITIAL VALUE PROBLEMS; NONLINEAR EQUATIONS; POLYNOMIALS;

EVOLUTION PDES; FINITE INTERVAL; GENERALIZED FOURIER TRANSFORMS; SPECTRAL TRANSFORMS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 26844577168     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxh047     Document Type: Article

References (13)

1. Akhiezer, N. I.&Glazman, I. M. (1966) Theory of Linear Operators in Hilbert Spaces. Moscow: Nauka.
2. Colin, T.&Ghidaglia, J. M. (2001) An initial-boundary value problem for the Korteweg-deVries equation posed on a finite interval. Adv. Diff. Eqns, 6, 1463-1492.
3. Dym, H.&McKean, H. P. (1972) Fourier Series and Integrals. New York: Academic.
4. Fokas, A. S. (1997) A unified transform method for solving linear and certain nonlinear PDE's. Proc. R. Soc. A, 453, 1411-1443.
5. Fokas, A. S. (2001) Two dimensional linear PDEs in a convex polygon. Proc. R. Soc. A, 457, 371-393.
6. Fokas, A. S. (2002) A new transform method for evolution PDEs. IMA J. Appl. Math., 67, 559-590.
7. Fokas, A. S.&PELLONI, B. (2001) Two-point boundary value problems for linear evolution equations. Proc. Camb. Phil. Soc., 17, 919-935.
8. Fokas, A. S.&SUNG, L. Y. (2004) Initial boundary value problems for linear evolution equations on the half line. Ann. Math., (in press).
9. Levin, B. Ja. (1972) Distribution of Zeros of Entire Functions. Translation of Mathematical Monographs. Providence, RI: AMS.
10. Pelloni, B. (2004a) Well-posed boundary value problems for linear evolution equations on a finite interval. Math. Proc. Camb. Phil. Soc., 136, 361-382.
11. Pelloni, B. (2004b) The spectral representation of two-point boundary value problems for linear PDEs. Submitted to Proc. R. Soc. A.
12. Titchmarsh, C. E. (1962) The Theory of Functions. Oxford: Oxford University Press.
13. Zhang, B. Y. (1999) Exact boundary controllability of the Korteweg-de Vries equation. SIAM J. Control Optim., 37, 543-565.