Integral Equations and Inverse Problems: (235 Pitman Research Notes in Mathematics Series)

The International Conference on Integral Equations and Inverse Problems was organized by the Bulgarian Academy of Sciences and was held September 18-23, 1989 in Varna, Bulgaria. Its purpose was to bring together a number of active mathematicians and numerical analysts currently involved in research in the integral equations, inverse problems and their numerical treatment and applications. Among the 120 participants there were scientists from Brazil, Japan, France, Sweden, USSR, China, FRG, Bulgaria and USA. As it can be seen from the table of contents of these proceedings, the present conference aims at bridging the gap between the mathematical and applied aspects of the integral equations and inverse problems. These proceedings include all presented for publication, invited lectures and some selected contributed talks. Also included are several invited talks not delivered at the Conference since technical obstacles made impossible their authors to attend it.

Table of Contents:
Spectral properties of elliptic operators of negative order, M.S.Agranovich; the highest order singularities of the scattering kernel, H.D.Alber; on the numerical solution of elliptic pseudodifferential equations on a smooth closed curve, B.A.Amosov; on the synthesis of field scattered by a perfectly conducting obstacle, V.Apel'tsin; scattering operator for Maxwell equations outside Schwarzschild black-hole, A.Bachelot; the estimates for the number of negative bound states of the Schrodinger operator for large coupling constants, M.S.Birman and M.Z.Solomjak; the inverse scattering problem for time harmonic electromagnetic waves, D.Coulton and P.Monk; about resolving power of inverse magneto-telluric problem, V.I.Dmitriev; Galerkin and collocation methods for partial integro-differential equations, G.Fairweather; inverse scattering problems for dissipative wave equation, V.Georgiev and Ya.Arnaoudov; numerical methods for a non-linear integral equation and an associated inverse problem, C.W.Groetsch; variational methods for boundary integral equations of the first kind, G.C.Hsiao; integral equation solution of some heat conduction problems, G.G.Hsiao and J.Saranen; on the low frequency asymptotics for exterior elasticity problems, G.C.Hsiao and W.L.Wendland; integral equations for the problems of waves diffraction on screens, A.S.Il'ynsky; on scattering matrices and zeta functions for several convex bodies, M.Ikawa; precise spectral asymptotics, V.Ivrii et al; on functions of the Schrodinger operator and a trace formula, A.Melin; reconstructing a function from its values on a subset of its domain - new sampling theorems, M.Z.Nashed and G.G.Walter; on the abstract inverse scattering problem for dissipative operators, H.Neidhardt; spectral properties of operators singularly depending on parameters and applications to mathematical physics, O.A.Oleinik; singularities of the scattering kernel for non-convex obstacles, V.M.Petkov; on an integral equation of the first kind arising from a cruciform crack problem, S.Prossdorf and A.Rathsfeld; high energy asymptotics for scattering phases for perturbations of Laplace operator, D.Robert; the inverse Sturm-Liouville problem for the spectral matrix on the whole axis and associated problems, F.S.Rofe-Beketov; eigenvalue asymptotics for the Schrodinger operator homogeneous magnetic potential and decreasing electric potential strong-electric-field approximation, G.D.Raikov; precise spectral asymptotics and inverse problems, Yu.G.Safarov; symbol construction and numerical analysis, B.Silberman, the scattering kernel of the elastic wave equation, H.Soga; some inverse problems in potential scattering, P.D.Stefanov; reduction of the Cauchy problem for elliptic equations to an extension problem, P.N.Vabishtchevich; part contents