Parametric excitation of high-mode oscillations for a non-linear telegraph equation

Journal Article · Thu Aug 31 00:00:00 EDT 2000 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2000V191N08ABEH000498; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21202957

Kolesov, Andrei Yu ^[1]; Rozov, Nikolai Kh ^[2]

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1. P.G. Demidov Yaroslavl State University, Yaroslavl (Russian Federation)
2. M.V. Lomonosov Moscow State University, Moscow (Russian Federation)

The problem of parametric excitation of high-mode oscillations is solved for a non-linear telegraph equation with a parametric external excitation and small diffusion. The equation is considered on a finite (spatial) interval with Neumann boundary conditions. It is shown that under a proper choice of parameters of the external excitation this boundary-value problem can have arbitrarily many exponentially stable solutions that are periodic in time and rapidly oscillate with respect to the spatial variable.

• OSTI ID: 21202957
• Journal Information: Sbornik. Mathematics, Vol. 191, Issue 8; Other Information: DOI: 10.1070/SM2000v191n08ABEH000498; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
BOUNDARY-VALUE PROBLEMS
DIFFUSION
EQUATIONS
EXCITATION
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
OSCILLATION MODES
PERIODICITY