Ebook: Direct and Inverse Problems of Mathematical Physics

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.

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The book consists of state-of-the-art chapters 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.
Audience: Researchers working in the field as well as scientists interested in the applications.

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The book consists of state-of-the-art chapters 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.
Audience: Researchers working in the field as well as scientists interested in the applications.
Content:
Front Matter....Pages i-vii
Algorithms of the Asymptotic Nonlinear Analysis....Pages 1-20
Transmission loss in a depth-varying ocean over a poroelastic seabed....Pages 21-37
Variations on (X,?) Duality....Pages 39-52
Uniqueness of Continuation Theorems....Pages 53-105
Determination of a Distributed Inhomogeneity in a Two-Layered Waveguide from Scattered Sound....Pages 107-124
Differentiability with Respect to Parameters of Integrated Semigroups....Pages 125-135
Boundedness of Pseudo-Differential Operators on H?rmander Spaces....Pages 137-147
Coefficient Identification in Elliptic Differential Equations....Pages 149-160
Quasi-Exponential Solutions for Some PDE with Coefficients of Limited Regularity....Pages 161-184
Analytically Smoothing Effect for Schr?dinger Type Equations with Variable Coefficients....Pages 185-219
Initial Boundary Value Problem for the Viscous Incompressible Flows....Pages 221-232
Initial-Boundary Value Problems for an Equation of Internal Waves in a Stratified Fluid....Pages 233-236
Homogenization of the System Equations of High Frequency Nonlinear Acoustics....Pages 237-250
Identification of a Reflection Boundary Coefficient in an Acoustic Wave Equation by Optimal Control Techniques....Pages 251-266
Numerical Solutions to Acoustic Scattering in Shallow Oceans by Periodic Wavelets....Pages 267-279
Solution of the Robin and Dirichlet Problem for the Laplace Equation....Pages 281-290
Existence and Decay of Solutions of Some Nonlinear Degenerate Parabolic Equations....Pages 291-300
On Regularity Results for Variational-Hemivariational Inequalities....Pages 301-322
An Inverse Problem in Elastodynamics....Pages 323-332
Singularities of the Reflected and Refracted Riemann Functions of Elastic Wave Propagation Problems in Stratified Media....Pages 333-342
Exact boundary controllability of a first order, non-linear hyperbolic equation with non-local integral terms arising in epidemic modeling....Pages 343-362
Singularities of solutions for nonlinear hyperbolic equations of second order....Pages 363-398
Positive Solutions of Semilinear Elliptic Boundary Value Problems in Chemical Reactor Theory....Pages 399-413
Fast Solvers of the Lippmann-Schwinger Equation....Pages 415-422
Inverse Source Problem for the Stokes System....Pages 423-440
Back Matter....Pages 441-451
....Pages 453-453