Steady-state oscillations in the continuously inhomogeneous medium described by the Ovsyannikov equation

  • Yu. A. Chirkunov


Using the group analysis methods, for the Ovsyannikov equation with maximal symmetry which describes steady-state oscillations in a continuous inhomogeneous medium, we obtain exact solutions to boundary-value problems for some regions (generalized Poisson formulas), which in particular can serve as test solutions for simulating steady-state oscillations in continuous inhomogeneous media. We find operators acting on the set of solutions in a one-parameter family of these equations.


Ovsyannikov equation maximal symmetry steady-state oscillations in continuous inhomogeneous medium intertwining operators generalized Poisson formulas 


  1. 1.
    L. V. Ovsyannikov, Group Analysis of Differential Equations (Nauka, Moscow, 1978) [in Russian].MATHGoogle Scholar
  2. 2.
    E. T. Wittaker and J. N. Wattson, Course of Modern Analysis, Vol. 2 (Nauka, Moscow, 1963) [in Russian].Google Scholar
  3. 3.
    F. Riesz and B. Szëkefalvi-Nagy, Lectures on Functional Analysis (Akadémiai Kiaó, Budapest, 1972; Mir, Moscow, 1979).Google Scholar
  4. 4.
    K. Miranda, Partial Differential Equations of Elliptic Type (Equazioni Alle Derivate Parziale Tipo Elliptico, Springer, Berlin, 1955; Inostrannaya Literatura, Moscow, 1957).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Novosibirsk State Technical UniversityNovosibirskRussia
  2. 2.Institute of Computational TechnologiesNovosibirskRussia

Personalised recommendations