Inverse Problems

1. Front Matter

   Pages 1-9

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2. The Linear Functional Strategy for Improperly Posed Problems

   • R. S. Anderssen

   Pages 11-30

3. Determination of a Source Term in a Linear Parabolic Differential Equation with Mixed Boundary Conditions

   • John R. Cannon, Yanping Lin

   Pages 31-49

4. Inverse Problems for Parabolic Partial Differential Equations

   • P. C. DuChateau

   Pages 51-59

5. Three-Dimensional Inverse Scattering

   • Margaret Cheney, James H. Rose, Brian DeFacio

   Pages 61-68

6. On Isospectral Gradient Flows — Solving Matrix Eigenprdblems using Differential Equations

   • Kenneth R. Driessel

   Pages 69-91

7. On an Integral Equation of the first Kind in Inverse Acoustic Scattering

   • Andreas Kirsch, Rainer Kress

   Pages 93-102

8. Approximation of Discrete Probability Distributions in Spherical Stereology

   • Rudolf Gorenflo

   Pages 103-115

9. Parameter Estimation for Distributed Systems Arising in Fluid Flow Problems via Time Series Methods

   • Tao Lin, Richard Ewing

   Pages 117-126

10. Analytic Solutions to the Inverse Problem of the Newtonian Potential

    • Carlo Domenico Pagani

    Pages 127-132

11. A Note on an Inverse Problem Related to the 3-D Heat Equation

    • John R. Cannon, Salvador Pérez Esteva

    Pages 133-137

12. Undetermined Coefficient Problems for Nonlinear Elliptic and Parabolic Equations

    • Michael Pilant, William Rundell

    Pages 139-154

13. The Method of ‘Generalized Interpolation’ for Approximate Solution of Ill-Posed Problems

    • Thomas I. Seidman

    Pages 155-161

14. Gel‘fan-Levitan’s theory and related inverse problems

    • Takashi Suzuki

    Pages 163-171

15. Reconstruction Ambiguities of Inverse Scattering on the Line

    • P. C. Sabatier

    Pages 173-192

The present volume contains manuscripts of lectures or topics related to the lectures which were given at the conference on "Inverse Problems" at the mathematical Research Institute at Oberwolfach. The conference took place during the week of May 18-24, 1986, and was managed by the editors. Recalling Professor Joseph Keller's paper entitled Inverse Problems, American Mathematical Monthly, 83 (1976), we give two direct quotes. "We call two problems inverses of one another if the formulation of each involves all or part of the solution of the other. Often, for historical reasons, one of the two problems has been studied extensively for some time, while the other is newer and not so well understood. In such cases, the former is called the direct problem, while the latter is called the inverse problem. " "The main sources of inverse problems are science and engineering. Often these problems concern the determination of the properties of some inaccess­ ible regions from observations on the boundary of that region. " Often, inverse problems are not well posed. This increases the difficulty in their analysis and numerical solution. As can be seen from the table of content of this volume, the conference covered inverse problems in scattering theory, seismology, tomography, estimation of coefficients and source terms in parabolic and elliptic differential equations, the inverse Sturm-Liouville problem, and numerical methods. The editors wish to thank Professor M. Barner and his co-workers of the Mathematical Research Institute for their help in creating the conference.

• differential equation
• partial differential equation
• scattering theory
• science

• Dept. Pure & Appl. Mathematics, Washington State University, Pullman, Washington, USA

  John Rozier Cannon

• Sonderforschungsbereich 72, Bonn 1, Germany

  Ulrich Hornung

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