Direct and Inverse Problems of Mathematical Physics

ISBN-13: 9780792360056 / Angielski / Twarda / 2000 / 453 str.

Robert P. Gilbert; Joji Kajiwara; R. P. Gilbert

Opis

This volume consists of papers presented in the special sessions on "Wave Phenomena and Related Topics," and "Asymptotics and Homogenization" of the ISAAC'97 Congress held at the University of Delaware, during June 2-7, 1997. The ISAAC Congress coincided with a U.S.-Japan Seminar also held at the University of Delaware. The latter was supported by the National Science Foundation through Grant INT -9603029 and the Japan Society for the Promotion of Science through Grant MTCS-134. It was natural that the 'participants of both meetings should interact and consequently several persons attending the Congress also presented papers in the Seminar. The success of the ISAAC Congress and the U.S.-Japan Seminar has led to the ISAAC'99 Congress being held in Fukuoka, Japan during August 1999. Many of the same participants will return to this Seminar. Indeed, it appears that the spirit of the U.S.-Japan Seminar will be continued every second year as part of the ISAAC Congresses. We decided to include with the papers presented in the ISAAC Congress and the U.S.-Japan Seminar several very good papers by colleagues from the former Soviet Union. These participants in the ISAAC Congress attended at their own expense. This volume has the title Direct and Inverse Problems of Mathematical Physics which consists of the papers on scattering theory, coefficient identification, uniqueness and existence theorems, boundary controllability, wave propagation in stratified media, viscous flows, nonlinear acoustics, Sobolev spaces, singularity theory, pseudo differential operators, and semigroup theory.

Spis treści

Preface. 1. Algorithms of the Asymptotic Nonlinear Analysis; A. Bruno. 2. Transmission Loss in a Depth-varying Ocean over a Poroelastic Seabed; J. Buchanan, R.P. Gilbert. 3. Variation on (chi, psi) Duality; R. Carroll. 4. Uniqueness of Continuation Theorems; M. Eller. 5. Determination of a Distributed Inhomogeneity in a Two-layer Waveguide from Scattered Sound; R.P. Gilbert, et al. 6. Differentiability with Respect to Parameters of Integrated Semigroups; M. He. 7. Coundedness of Pseudo-differential Operators on Hörmander Spaces; G. Iancu. 8. Coefficient Identification in Elliptic Differential Equations; I. Knowles. 9. Quasi-exponential Solutions for Some PDE with Coefficients of Limited Regularity; A. Panchenko. 10. Analytically Smoothing Effect for Schrödinger Type Equations with Variable Coefficients; K. Kajitani, W. Wakabayashi. 11. Initial Boundary Value Problem for the Viscous Incompressible Flows; H. Kato. 12. Initial-boundary Value Problems for an Equation of Internal Waves in a Stratified Fluid; P. Krutitskii. 13. Homogenization of the System Equations of High Frequency Nonlinear Acoustics; E.A. Lapshin, G.P. Panasenko. 14. Identification of a Reflection Boundary Coefficient in an Acoustic Wave Equation by Optimal Control Techniques; S. Lenhart, et al. 15. Numerical Solutions to Acoustic Scattering in Shallow Oceans by Periodic Wavelets; W. Lin, X. Wang. 16. Solution of the Robin and Dirichlet Problem for the Laplace Equation; D. Medkova. 17. Existence and Decay of Solutions of someNonlinear Degenerate Parabolic Equations; T. Nanbu. 18. On Regularity Results for Variational-hemivariational Inequalities; Z. Naniewicz, P.D. Panagiotoopoulos. 19. Quasi-exponential Solutions for some PDE with Coefficients of Limited Regularity; A. Panchenko. 20. An Inverse Problem in Elastodynamics; L. Rachele. 21. Denseness of Co∞(RN) in the Generalized Sobolev Spaces; S. Samko. 22. Singularities of Reflected and Refracted Riemann Functions of Elastic Wave Propagation Problems in Stratified Media; S. Shimizu. 23. Exact Boundary Controllability of a First Order, Non-linear Hyperbolic Equation with Non-local Integral Terms Arising in Epidemic Modeling; I. Lasiecka, R. Triggiani. 24. Singularities of Solutions for Nonlinear Hyperbolic Equations of Second Order; M. Tsuji. 25. Positive Solutions of Semilinear Elliptic Boundary Value Problems in Chemical Reactor Theory; K. Umezu, K. Taira. 26. Fast Solvers of the Lippman-Schwinger Equation; G. Vainikko. 27. Inverse Source Problems for the Stokes System; M. Yamamota, O.Y. Imanuvilov.