Existence and Asymptotic Behavior of Beam-Equation Solutions with Strong Damping and p(x)-Biharmonic Operator
DOI:
https://doi.org/10.15407/mag18.04.488Анотація
У цiй роботi ми розглядаємо нелiнiйне рівняння балки із сильним демпфуванням та p(x)-бiгармонiчний оператор. Показник нелiнiйностi p(·) є заданою функцiєю, яка задовольняє певнi умови. Застосовуючи метод Фаедо–Ґалеркiна, ми довели iснування слабких розв’язкiв. Застосовуючи лему Такао, ми встановили асимптотичне поводження слабких розв’язкiв за м’яких припущень щодо показника p(·). Ми доводимо, що асимптотичне поводження слабкого розв’язку є експоненцiйно i алгебраїчно залежним вiд змiнного показника. Ця робота полiпшує та узагальнює багато iнших результатiв згаданих в лiтературi.
Mathematical Subject Classification 2010: 35A01, 35B40, 35D30, 35L25
Ключові слова:
слабки розв’язки, iснування, асимптотичне поводження, рiвняння балки, p(x)-бiгармонiчний оператор, змiнний показникПосилання
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