The limiting amplitude principle for the nonlinear Lamb system

Dudnikova, T. V.

doi:10.15393/j3.art.2019.6571

Cited by 1 publication

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“…This theorem is proved in [3]. We prove the similar result in the case ̸ = 0 under additional restrictions on the function ( ) (see Section 3).…”

Section: ∫︁supporting

confidence: 53%

The asymptotic behavior of solutions to the Cauchy problem with periodic initial data for the nonlinear Lamb system

Dudnikova

2018

KIAM Prepr.

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О р д е н а Л е н и н а ИНСТИТУТ ПРИКЛАДНОЙ МАТЕМАТИКИ имени М. В. КЕЛДЫША Р о с с и й с к о й а к а д е м и и н а у к T. V. Dudnikova The asymptotic behavior of solutions to the Cauchy problem with periodic initial data for the nonlinear Lamb system Москва-2018 Дудникова Т.В. Асимптотическое поведение решений задачи Коши с периодическими начальными данными для нелинейной системы Лэмба Рассматривается модель, состоящая из бесконечной струны, взаимодействующей с нелинейным осциллятором. Для нее изучается задача Коши с периодическими начальными данными. Основная цель-доказать сходимость решений при → ∞ к периодическим по времени решениям. Ключевые слова: нелинейная система Лэмба, задача Коши, периодические начальные данные, принцип предельной амплитуды Tatiana Vladimirovna Dudnikova The asymptotic behavior of solutions to the Cauchy problem with periodic initial data for the nonlinear Lamb system A model consisting of an infinite string coupled to a nonlinear oscillator is considered. The Cauchy problem for the system with the periodic initial data is studied. The main goal is to prove the convergence of the solutions as → ∞ to time periodic solutions.

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“…This theorem is proved in [3]. We prove the similar result in the case ̸ = 0 under additional restrictions on the function ( ) (see Section 3).…”

Section: ∫︁supporting

confidence: 53%

The asymptotic behavior of solutions to the Cauchy problem with periodic initial data for the nonlinear Lamb system

Dudnikova

2018

KIAM Prepr.

View full text Add to dashboard Cite

show abstract

The limiting amplitude principle for the nonlinear Lamb system

Abstract: 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 time periodic solutions.

Cited by 1 publication

References 12 publications

The asymptotic behavior of solutions to the Cauchy problem with periodic initial data for the nonlinear Lamb system

The asymptotic behavior of solutions to the Cauchy problem with periodic initial data for the nonlinear Lamb system

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