An inverse problem for the forced transverse vibration of a rectangular membrane with time dependent potential

Year 2020, Volume: 22 Issue: 65, 599 - 610, 15.05.2020

İbrahim Tekin

https://doi.org/10.21205/deufmd.2020226525

Abstract

In this
paper, an initial-boundary value problem for a two-dimensional wave equation which
arises in the equation of motion for the forced transverse vibration of a
rectangular membrane is considered. Giving an additional condition, a
time-dependent coefficient is determined and existence and uniqueness theorem
for small times is proved. Moreover, characterization of the conditional
stability is given and numerical solution of the inverse problem investigated
by using finite difference method.

Keywords

Inverse problem, Fourier method, Two dimensional wave equation, Finite difference method

Zamana bağlı potansiyeli olan dikdörtgen bir zarın zorlanmış çapraz titreşimi için bir ters problem

Abstract

Bu çalışmasa,
dikdörtgen bir zarın zorlanmış enine titreşimi için hareket denkleminde ortaya
çıkan iki boyutlu bir dalga denklemi için başlangıç-sınır değer problemi ele
alınmıştır. Verilmiş bir ek koşul  ile
zamana bağlı katsayı belirlenmiştir ve yeteri kadar küçük zaman değerleri için
varlık ve teklik teoremi ispatlanmıştır. Ayrıca, koşullu kararlılığın
karakterizasyonu verilmiş ve ters problemin sayısal çözümü sonlu farklar
yöntemi kullanılarak incelenmiştir.

Keywords

Ters problem, Fourier yöntemi, İki boyutlu dalga denklemi, Sonlu farklar yöntemi

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