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.
📌 3 Key Takeaways
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Objective & Hypothesis:The paper focuses on an inverse problem for a nonlinear hyperbolic equation with periodic boundary conditions and a time-dependent coefficient.
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Key Findings & Data:The paper focuses on an inverse problem for a nonlinear hyperbolic equation with periodic boundary conditions and a time-dependent coefficient.
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Conclusion & Impact: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.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Devirli Sınır Koşulu · Ters Problem · Lineer olmayan hiperbolik denklem
Abstract
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.
Özet
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.
Strauss, W. A. (2008). Partial Differential Equations (2nd ed.). Wiley, United States of America.
Whitham, G. B. (1974). Linear and Nonlinear Waves. Wiley.
Romanov, V. G. (1987). Inverse Problems of Mathematical Physics (1st ed.). VSP, Utrecht.
Bukhgeim, A. L., Klibanov, M. V. (2002). Inverse Problems in Partial Differential Equations. Springer, New York.
Kabanikhin, S. I. (2011). Inverse and Ill-posed Problems: Theory and Applications. Inverse and Ill-Posed Problems Series, Vol. 55. De Gruyter.
Hill, G. W. (1886). On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon. Acta Mathematica, 8, 1–36.
Kanca, F., Bağlan, I. (2018). Inverse problem for Euler–Bernoulli equation with periodic boundary condition. Filomat, 32(16), 5691–5705.
Mansur, I., Tekin, I. (2016). Inverse coefficient problems for a first order hyperbolic system. Applied Numerical Mathematics, 106, 98–115.
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.