02253cam a22002898a 4500991000166089707536090406s2008 pau b 001 0 eng d9780898716511b13821672-39ule_instDip.to Fisicaeng515/.3522LC QA37953.1.5Fokas, A. S.629884A unified approach to boundary value problems /Athanassios S. Fokas0809xv, 336 p. ;24 cmCBMS-NSF regional conference series in applied mathematics ;78Includes bibliographical references and indexA new transform method for linear evolution equations -- Evolution equations on the half line -- Evolution equations on the finite interval -- Asymptotics and a novel numerical technique -- Analyitic inversion of integrals -- From PDEs to classical transforms -- Riemann-Hilbert and d-bar problems -- The Fourier transform and its variations -- The inversion of the attenuated radon transform and medical imaging -- The Dirichlet to Neumann map for a moving boundary -- Novel integral representations for linear boundary value problems -- Divergence formulation, the global relation, and lax pairs -- Rederivation of the integral representations on the half-line and the finite interval -- The basic elliptic PDEs in a polygonal domain -- Novel analytical and numerical methods for elliptic PDEs in a convex polygon -- The new transform method for elliptic PDEs in simple polygonal domains -- Formulation of Riemann-Hilbert problems -- A collocation method in the Fourier plane -- Integrable nonlinear PDEs -- From linear to integrable nonlinear PDEs -- Nonlinear integrable PDEs on the half-line -- Linearizable boundary conditions -- The generalized Dirichlet to Neumann map -- Asymptotics of oscillatory Riemann-Hilbert problemsBoundary value problems.b1382167228-01-1406-04-09991000166089707536LE006 53.1.5 FOK12006000162944le006pE52.18-l- 01010.i1495091106-04-09Unified approach to boundary value problems1225254UNISALENTOle00606-04-09ma -engpau20