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

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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