A Unified Approach to Boundary Value Problems

Preface; Introduction; 1. Evolution equations on the half-line; 2. Evolution equations on the finite interval; 3. Asymptotics and a novel numerical technique; 4. From PDEs to classical transforms; 5. Riemann–Hilbert and d-Bar problems; 6. The Fourier transform and its variations; 7. The inversion of the attenuated Radon transform and medical imaging; 8. The Dirichlet to Neumann map for a moving boundary; 9. Divergence formulation, the global relation, and Lax pairs; 10. Rederivation of the integral representations on the half-line and the finite interval; 11. The basic elliptic PDEs in a polygonal domain; 12. The new transform method for elliptic PDEs in simple polygonal domains; 13. Formulation of Riemann–Hilbert problems; 14. A collocation method in the Fourier plane; 15. From linear to integrable nonlinear PDEs; 16. Nonlinear integrable PDEs on the half-line; 17. Linearizable boundary conditions; 18. The generalized Dirichlet to Neumann map; 19. Asymptotics of oscillatory Riemann–Hilbert problems; Epilogue; Bibliography; Index.