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Inverse scattering problem for moving obstacles

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References

  1. Cardoso, F., Petkov, V.: Leading singularity of the scattering kernel for moving obstacles with dissipative boundary condition. Boll. Unione Mat. Ital., VII. Ser.4-B, 567–589 (1990)

    MathSciNet  Google Scholar 

  2. Colton D., Kress, R.: Integral Equation Methods in Scattering Theory. New York: Wiley 1983

    MATH  Google Scholar 

  3. Cooper, J.: Local decay of solutions of the wave equation in the exterior of a moving body. J. Math. Anal. Appl.49, 130–153 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cooper, J.: Scattering of plane waves by a moving obstacle. Arch. Ration. Mech. Anal.71, 113–149 (1979)

    Article  MATH  Google Scholar 

  5. Cooper, J.: Scattering frequencies for time-periodic scattering problems. (Lect. Notes Math. vol. 1223, pp. 37–48). Berlin Heidelberg New York: Springer 1986

    Google Scholar 

  6. Cooper, J., Strauss, W.: Energy boundedness and decay of waves reflecting off a moving obstacle. Indiana Univ. Math. J.25, 671–690 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  7. Cooper, J., Strauss, W.: Representation of the scattering operator for moving obstacles. Indiana Univ. Math. J.28, 643–671 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  8. Cooper, J., Strauss, W.: Scattering of waves by periodically moving bodies. J. Funct. Anal.47, 180–229 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  9. Cooper, J., Strauss, W.: The leading singularity of a wave reflected by a moving boundary. J. Differ. Equations52, 175–203 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  10. Cooper, J., Strauss, W.: Abstract scattering theory for time periodic systems with applications to electromagnetism. Indiana Univ. Math. J.34, 33–83 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  11. Cooper, J., Strauss, W.: Time-periodic scattering of symmetric hyperbolic systems. J. Math. Anal. Appl.122, 444–452 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hirsh, M.: Differential Topology. New York Heidelberg Berlin: Springer 1976

    Google Scholar 

  13. Hörmander, L.: The Analysis of Linear Partial Differential Operators, vol. 1. New York Heidelberg Berlin: Springer 1983

    Google Scholar 

  14. Lax, P., Phillips, R.: Scattering Theory, New York: Academic Press 1967

    MATH  Google Scholar 

  15. Majda, A.: High frequency asymptotics for the scattering matrix and the inverse problem of acoustical scattering. Commun. Pure Appl. Math.29, 261–291 (1976)

    MATH  MathSciNet  Google Scholar 

  16. Majda, A.: A representation formula for the scattering operator and the inverse problem for arbitrary bodies. Commun. Pure Appl. Math.30, 165–194 (1977)

    MATH  MathSciNet  Google Scholar 

  17. Petkov, V.: Scattering Theory for Hyperbolic Operators. North Holland 1989

  18. Petkov, V., Georgiev, V.: RAGE theorem for power bounded operators and decay of local energy for moving obstacles. Ann. Inst. Henry Poincaré, Phys. Thèor.51, 155–185 (1989)

    MATH  MathSciNet  Google Scholar 

  19. Petkov, V., Rangelov, Tz.: Leading singularity of the scattering kernel for moving obstacles. Math. Balk., New Ser.4, 91–112 (1990)

    MATH  MathSciNet  Google Scholar 

  20. Popov, G., Rangelov, Tz.: Exponential growth of the local energy for moving obstacles. Osaka J. Math.26, 881–895 (1989)

    MATH  MathSciNet  Google Scholar 

  21. Ramm, A.G.: Scattering by Obstacles. Dordrecht: Reidel 1986

    MATH  Google Scholar 

  22. Soga, H.: Conditions against rapid decrease of oscillatory integrals and their applications to inverse scattering problems. Osaka J. Math.23, 441–456 (1986)

    MATH  MathSciNet  Google Scholar 

  23. Strauss, W.: The existence of the scattering operator for moving obstacles. J. Funct. Anal.31, 255–262 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  24. Stefanov, P.: Uniqueness of the inverse scattering problem for the wave equation with a potential depending on time. Inverse Probl.4, 913–920 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  25. Stefanov, P.: Uniqueness of the multi-dimensional inverse scattering problem for time-dependent potentials. Math. Z.201, 541–559 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  26. Tamura, H.: On the decay of the local energy for wave equations with a moving obstacle. Nagoya Math. J.71, 125–147 (1978)

    MATH  MathSciNet  Google Scholar 

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Partially supported by Bulgarian Ministry of Culture, Science and Eduction, Grant 52

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Stefanov, P.D. Inverse scattering problem for moving obstacles. Math Z 207, 461–480 (1991). https://doi.org/10.1007/BF02571402

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