Direct and Inverse Problems of Mathematical Physics

1. Front Matter

   Pages i-vii

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2. Algorithms of the Asymptotic Nonlinear Analysis

   • Alexander D. Bruno

   Pages 1-20

3. Transmission loss in a depth-varying ocean over a poroelastic seabed

   • James L. Buchanan, Robert P. Gilbert

   Pages 21-37

4. Variations on (X,ψ) Duality

   • Robert Carroll

   Pages 39-52

5. Uniqueness of Continuation Theorems

   • Matthias M. Eller

   Pages 53-105

6. Determination of a Distributed Inhomogeneity in a Two-Layered Waveguide from Scattered Sound

   • Robert P. Gilbert, Christopher Mawata, Yongzhi Xu

   Pages 107-124

7. Differentiability with Respect to Parameters of Integrated Semigroups

   • Min He

   Pages 125-135

8. Boundedness of Pseudo-Differential Operators on Hörmander Spaces

   • G. M. Iancu

   Pages 137-147

9. Coefficient Identification in Elliptic Differential Equations

   • Ian Knowles

   Pages 149-160

10. Quasi-Exponential Solutions for Some PDE with Coefficients of Limited Regularity

    • Alexander Panchenko

    Pages 161-184

11. Analytically Smoothing Effect for Schrödinger Type Equations with Variable Coefficients

    • Kunihiko Kajitani, Seiichiro Wakabayashi

    Pages 185-219

12. Initial Boundary Value Problem for the Viscous Incompressible Flows

    • Hisako Kato

    Pages 221-232

13. Initial-Boundary Value Problems for an Equation of Internal Waves in a Stratified Fluid

    • P. A. Krutitskii

    Pages 233-236

14. Homogenization of the System Equations of High Frequency Nonlinear Acoustics

    • Evgueny A. Lapshin, Gregory P. Panasenko

    Pages 237-250

15. Identification of a Reflection Boundary Coefficient in an Acoustic Wave Equation by Optimal Control Techniques

    • Suzanne Lenhart, Vladimir Protopopescu, Jiongmin Yong

    Pages 251-266

16. Numerical Solutions to Acoustic Scattering in Shallow Oceans by Periodic Wavelets

    • Wei Lin, Xianbiao Wang

    Pages 267-279

17. Solution of the Robin and Dirichlet Problem for the Laplace Equation

    • Dagmar Medková Praha

    Pages 281-290

18. Existence and Decay of Solutions of Some Nonlinear Degenerate Parabolic Equations

    • Tokumori Nanbu

    Pages 291-300

19. On Regularity Results for Variational-Hemivariational Inequalities

    • Z. Naniewicz, P. D. Panagiotopoulos

    Pages 301-322

20. An Inverse Problem in Elastodynamics

    • Lizabeth V. Rachele

    Pages 323-332

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.

• Boundary value problem
• Sobolev space
• acoustic wave equation
• algorithms
• hyperbolic equation
• mathematical physics
• scattering theory
• wave equation
• partial differential equations

• University of Delaware, USA

  Robert P. Gilbert

• Kyushu University, Japan

  Joji Kajiwara

• University of Tennessee at Chattanooga, USA

  Yongzhi S. Xu

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