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

Article

Abstract

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.

Keywords

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

References

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    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

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