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Averaging operators and real equations of hydromechanics

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Pseudodifferential operators occurring in real equations of continuous-medium mechanics are discussed.

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References

  1. R. R. Aidagulov and M. V. Shamolin, “A phenomenological approach to finding interphase forces,” Dokl. Ross. Akad. Nauk, 412, No. 1, 44–47 (2007).

    MathSciNet  Google Scholar 

  2. R. R. Aidagulov and M. V. Shamolin, “A general spectral approach to continuous medium dynamics,” Sovremennaya Matematika. Fundamental’nye Napravleniya, 23, 52–70 (2007).

    Google Scholar 

  3. R. F. Ganiev, L. E. Ukrainskii, and O. R. Ganiev “Resonant filtration flows in a porous medium saturated with a fluid,” Dokl. Ross. Akad. Nauk, 412, No. 1 (2007).

    Google Scholar 

  4. F. John, Plane Waves and Spherical Means Applied to Partial Differential Equations [Russian translation], IL, Moscow (1958).

    Google Scholar 

  5. A. G. Kulikovskii and E. I. Sveshnikova, Nonlinear Waves in Elastic Media [in Russian], Moskovskii Lizei, Moscow (1998).

    Google Scholar 

  6. A. A. Lokshin and Yu. V. Suvorova, Mathematical Theory of Wave Propagation in Media With Memory [in Russian], MGU, Moscow (1982).

    MATH  Google Scholar 

  7. A. N. Osiptsov, “On accounting for volume finiteness and hydrodynamic interaction of particles in gas suspensions,” Dokl. Akad. Nauk SSSR, 275, No. 5, 1073–1076 (1984).

    Google Scholar 

  8. R. Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe [Russian translation], Reg. Khaotic Dinamik, Moscow–Izhevsk (2007).

    Google Scholar 

  9. V. Ya. Rudyak, Statistical Theory of Dissipative Processes in Gases and Fluids [in Russian], Nauka, Novosibirsk (1987).

    Google Scholar 

  10. M. Sato, “Theory of hyperfunctions. I, II,” J. Fac. Shi. Univ. Tokyo, Sect. I, 139–193 (1959); 387–437 (1960).

  11. M. V. Shamolin, Some Problems of Differential and Topological Diagnosis [in Russian], 2nd Revised and Supplemented Edition, Ekzamen, Moscow (2007), pp. 240–281.

    Google Scholar 

  12. M. A. Shubin, Pseudodifferential Operators and Spectral Theory [in Russian], Nauka, Moscow (1979).

    Google Scholar 

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Correspondence to M. V. Shamolin.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 65, Mathematical Physics, Combinatorics, and Optimal Control, 2009.

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Aidagulov, R.R., Shamolin, M.V. Averaging operators and real equations of hydromechanics. J Math Sci 165, 637–653 (2010). https://doi.org/10.1007/s10958-010-9833-0

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  • DOI: https://doi.org/10.1007/s10958-010-9833-0

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