Boundary-value problems for linear PDEs with variable coefficients

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 460, Issue 2044, 2004, Pages 1131-1151

  Fokas, A S ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Laplace; Riemann Hilbert; Variable coefficient

Indexed keywords

ARTICLE; CORRELATION COEFFICIENT; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; METHODOLOGY; NONLINEAR SYSTEM;

EID: 1642525814     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2003.1208     Document Type: Article

References (16)

1. Deift, P. & Zhou, X. 1991 Direct and inverse scattering on the line with arbitrary singularities. Commun. Pure Appl. Math. 44, 485-533.
2. Deift, P., Tomei, C. & Trubowitz, E. 1982 Inverse scattering and the Boussinesq equation. Commun. Pure Appl. Math. 35, 567-628.
3. Faddeev, L. D. 1964 The properties of the S-matrix of the one-dimensional Schrödinger equation. Proc. Steklov Institute Math. 73, 314-333.
4. Fokas, A. S. 1997 A unified transform method for solving linear and certain nonlinear PDEs. Proc. R. Soc. Lond. A 453, 1411.
5. Fokas, A. S. 2001 Two-dimensional PDEs in a convex polygon. Proc. R. Soc. Lond. 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. & Kapaev, A. A. 2003 A transform method for the Laplace equation in a polygon. IMA J. Appl. Math. 68, 1-55.
8. Fokas, A. S. & Pelloni, B. 2000 Integral transforms, spectral representations and the d-bar problem. Proc. R. Soc. Lond. A 456, 805-833.
9. Fokas, A. S. & Schultz, P. 2003 Long-time asymptotics of moving boundary problems using an Ehrenpreis-type representation and its Riemann-Hilbert nonlinearization. Commun. Pure Appl. Math. 55, 517-548.
10. Fokas, A. S. & Sung, L. Y. 2004 Initial boundary-value problems for integrable evolution equations on the half line. Ann. Math. (In the press.)
11. Fokas, A. S. & Zyskin, M. 2002 The fundamental differential form and boundary-value problems. Q. J. Mech. Appl. Math. 55, 457-479.
12. Fulton, S., Fokas, A. S. & Xenophontos, C. 2004 An analytical method for linear elliptic PDEs and its numerical implementation. J. Comput. Appl. Math. (In the press.)
13. Pelinovsky, D. E. & Sulem, C. 2000a Spectral decomposition for the Dirac system associated to the DSII equation. Inverse Problems 16, 59-74.
14. Pelinovsky, D. E. & Sulem, C. 2000b Eigenfunctions and eigenvalues for a scalar Riemann-Hilbert problem associated to inverse scattering. Commun. Math. Phys. 208, 713-760.
15. Titchmarsh, E. C. 1962 Eigenfunction expansions associated with second-order differential equations. I. Oxford University Press.
16. Zhang, B.-Y. 1999 Exact boundary controllability of the KdV equation. SIAM J. Control Optimiz. 37, 543-565.