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Homogenization of the Integro-Differential Burgers Equation

  • A. Amosov
  • G. Panasenko
Chapter

Abstract

The Burgers equation is a fundamental partial differential equation of fluid mechanics and acoustics. It occurs in various areas of applied mathematics, such as the modeling of gas dynamics and traffic flow (see [Ho50] and [Co51]).

Keywords

Acoustics 
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References

  1. [AmPa09]
    Amosov, A., Panasenko, G.: Integro-differential Burgers equation. Solvability and homogenization. SIAM J. Math. Anal. (submitted).Google Scholar
  2. [Co51]
    Cole, J.D.: On a quasilinear parabolic equation occurring in aerodynamics. Quart. Appl. Math., 9, 225–236 (1951).MATHMathSciNetGoogle Scholar
  3. [Ho50]
    Hopf, E.: The partial differential equation u t+uu x = μu xx. Comm. Pure Appl. Math., 3, 201–230 (1950).MATHCrossRefMathSciNetGoogle Scholar
  4. [La97]
    Landa, P.S.: Nonlinear Oscillations and Waves, Nauka, Moscow (1997) (Russian).Google Scholar
  5. [PaPs08]
    Panasenko, G., Pshenitsyna, N.: Homogenization of an integro-differential equation of Burgers type. Applicable Anal., 87, 1325–1336 (2008).MATHCrossRefMathSciNetGoogle Scholar
  6. [PoSo62]
    Poliakova, A.L., Soluyan, S.I., Khokhlov, R.V.: On propagation of finite perturbations in media with relaxation. Acoustic J., 8, 107–112 (1962).Google Scholar
  7. [RuSo75]
    Rudenko, O.V., Soluyan, S.I.: Theoretical Foundations of Nonlinear Acoustics, Nauka, Moscow (1975) (Russian).Google Scholar

Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Moscow Power Engineering Institute (Technical University)MoscowRussia
  2. 2.Université de Saint-ÉtienneSaint-ÉtienneFrance

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