Well-Posedness Analysis for an Inverse Coefficient Nonlinear Wave Equation

Öz

The paper focuses on an inverse problem for a nonlinear hyperbolic equation with periodic boundary conditions and a time-dependent coefficient. By employing the Fourier method, both the solution and the coefficient function are determined, while the convergence of the iterative algorithm guarantees the uniqueness and stability of the solution.

Anahtar Kelimeler

• Inverse problem
• Nonlinear hyperbolic equation
• Periodic boundary conditions.

Ters Katsayılı Doğrusal Olmayan Dalga Denklemi için İyi Tanımlılık Analizi

Öz

Bu makale, periyodik sınır koşulları ve zamana bağlı bir katsayıya sahip doğrusal olmayan bir hiperbolik denklem için ters bir probleme odaklanmaktadır. Fourier yöntemi kullanılarak hem çözüm hem de katsayı fonksiyonu belirlenirken, yinelemeli algoritmanın yakınsaması çözümün benzersizliğini ve kararlılığını garanti altına almaktadır.

Anahtar Kelimeler

• Devirli Sınır Koşulu
• Ters Problem
• Lineer olmayan hiperbolik denklem

Kaynakça

1. 1. Strauss, W. A. (2008). Partial Differential Equations (2nd ed.). Wiley, United States of America.
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9. 9. Bağlan, I., Kanca, F. (2013). An inverse coefficient problem for a quasilinear parabolic equation with periodic boundary and integral overdetermination condition. Mathematical Methods in the Applied Sciences, 38(5), 851–867.