Abstract
Pseudodifferential operators occurring in real equations of continuous-medium mechanics are discussed.
Similar content being viewed by others
References
R. R. Aidagulov and M. V. Shamolin, “A phenomenological approach to finding interphase forces,” Dokl. Ross. Akad. Nauk, 412, No. 1, 44–47 (2007).
R. R. Aidagulov and M. V. Shamolin, “A general spectral approach to continuous medium dynamics,” Sovremennaya Matematika. Fundamental’nye Napravleniya, 23, 52–70 (2007).
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).
F. John, Plane Waves and Spherical Means Applied to Partial Differential Equations [Russian translation], IL, Moscow (1958).
A. G. Kulikovskii and E. I. Sveshnikova, Nonlinear Waves in Elastic Media [in Russian], Moskovskii Lizei, Moscow (1998).
A. A. Lokshin and Yu. V. Suvorova, Mathematical Theory of Wave Propagation in Media With Memory [in Russian], MGU, Moscow (1982).
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).
R. Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe [Russian translation], Reg. Khaotic Dinamik, Moscow–Izhevsk (2007).
V. Ya. Rudyak, Statistical Theory of Dissipative Processes in Gases and Fluids [in Russian], Nauka, Novosibirsk (1987).
M. Sato, “Theory of hyperfunctions. I, II,” J. Fac. Shi. Univ. Tokyo, Sect. I, 139–193 (1959); 387–437 (1960).
M. V. Shamolin, Some Problems of Differential and Topological Diagnosis [in Russian], 2nd Revised and Supplemented Edition, Ekzamen, Moscow (2007), pp. 240–281.
M. A. Shubin, Pseudodifferential Operators and Spectral Theory [in Russian], Nauka, Moscow (1979).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 65, Mathematical Physics, Combinatorics, and Optimal Control, 2009.
Rights and permissions
About this article
Cite this article
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
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-010-9833-0