Forced Frequency Locking for Semilinear Dissipative Hyperbolic PDEs

Autor: Irina Kmit, Lutz Recke
Rok vydání: 2022
Předmět:
Zdroj: Journal of Dynamics and Differential Equations.
ISSN: 1572-9222
1040-7294
DOI: 10.1007/s10884-022-10236-0
Popis: This paper concerns the behavior of time-periodic solutions to 1D dissipative autonomous semilinear hyperbolic PDEs under the influence of small time-periodic forcing. We show that the phenomenon of forced frequency locking happens similarly to the analogous phenomena known for ODEs or parabolic PDEs. However, the proofs are essentially more difficult than for ODEs or parabolic PDEs. In particular, non-resonance conditions are needed, which do not have counterparts in the cases of ODEs or parabolic PDEs. We derive a scalar equation which answers the main question of forced frequency locking: Which time shifts of the solution to the unforced equation do survive under which forcing?
Comment: 47 pages
Databáze: OpenAIRE
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