Steady-state oscillations in continuously inhomogeneous medium described by the Ovsyannikov equation. (Russian) Zbl 1240.35011
Summary: For the Ovsyannikov equation possessing the maximal symmetry and describing steady state oscillations in continuously inhomogeneous medium, the group analysis methods yield exact solutions to boundary value problems for some domains (generalized Poisson formulas), which, in particular, can serve as test solutions in simulating steady state oscillations in continuously inhomogeneous media. The operators are found that are valid on the set of solutions in every one-parameter family of such equations.
MSC:
| 35B06 | Symmetries, invariants, etc. in context of PDEs |
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 35G20 | Nonlinear higher-order PDEs |
| 35E20 | General theory of PDEs and systems of PDEs with constant coefficients |
