Geodesic
The limiting amplitude principle for the nonlinear Lamb system
Problemy analiza, Tome 8 (2019) no. 3, pp. 45-62

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A system consisting of an infinite string coupled to a nonlinear oscillator is considered. For the system, the Cauchy problem with the periodic initial data is studied. The main goal is to prove the convergence of the solutions as $t\to\infty$ to time periodic solutions.
Keywords: the nonlinear Lamb system, the Cauchy problem, periodic initial data, the limiting amplitude principle. 
@article{PA_2019_8_3_a4,
     author = {T. V. Dudnikova},
     title = {The limiting amplitude principle for the nonlinear {Lamb} system},
     journal = {Problemy analiza},
     pages = {45--62},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2019_8_3_a4/}
}
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T. V. Dudnikova. The limiting amplitude principle for the nonlinear Lamb system. Problemy analiza, Tome 8 (2019) no. 3, pp. 45-62. http://geodesic.mathdoc.fr/item/PA_2019_8_3_a4/