Existence and Asymptotic Behavior of Beam-Equation Solutions with Strong Damping and p(x)-Biharmonic Operator

Автор(и)

  • Jorge Ferreira Department of Exact Sciences, Federal Fluminense University, Av. dos Trabalhadores 420, Volta Redonda, 27255-125, Brazil
  • Willian S. Panni Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, Covilhã, 6201-001, Portugal
  • Salim A. Messaoudi Department of Mathematics, University of Sharjah, Sharjah, P. O. Box 27272, United Arab Emirates
  • Erhan Pişkin Department of Mathematics, Dicle University, 21280 Diyarbakır, Turkey
  • Mohammad Shahrouzi Department of Mathematics, Jahrom University, Jahrom, P. O. Box 74137-66171, Iran

DOI:

https://doi.org/10.15407/mag18.04.488

Ключові слова:

слабки розв’язки, iснування, асимптотичне поводження, рiвняння балки, p(x)-бiгармонiчний оператор, змiнний показник

Анотація

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

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Ferreira, J.; Panni, W. S.; Messaoudi, S. A.; Pişkin, E.; Shahrouzi, M. Existence and Asymptotic Behavior of Beam-Equation Solutions with Strong Damping and p(x)-Biharmonic Operator. Журн. мат. фіз. анал. геом. 2022, 18, 488-513.

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