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.
Kaynakça
- 1. Strauss, W. A. (2008). Partial Differential Equations (2nd ed.). Wiley, United States of America.
- 2. Whitham, G. B. (1974). Linear and Nonlinear Waves. Wiley.
- 3. Romanov, V. G. (1987). Inverse Problems of Mathematical Physics (1st ed.). VSP, Utrecht.
- 4. Bukhgeim, A. L., Klibanov, M. V. (2002). Inverse Problems in Partial Differential Equations. Springer, New York.
- 5. Kabanikhin, S. I. (2011). Inverse and Ill-posed Problems: Theory and Applications. Inverse and Ill-Posed Problems Series, Vol. 55. De Gruyter.
- 6. 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.
- 7. Kanca, F., Bağlan, I. (2018). Inverse problem for Euler–Bernoulli equation with periodic boundary condition. Filomat, 32(16), 5691–5705.
- 8. Mansur, I., Tekin, I. (2016). Inverse coefficient problems for a first order hyperbolic system. Applied Numerical Mathematics, 106, 98–115.
- 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.
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. Strauss, W. A. (2008). Partial Differential Equations (2nd ed.). Wiley, United States of America.
- 2. Whitham, G. B. (1974). Linear and Nonlinear Waves. Wiley.
- 3. Romanov, V. G. (1987). Inverse Problems of Mathematical Physics (1st ed.). VSP, Utrecht.
- 4. Bukhgeim, A. L., Klibanov, M. V. (2002). Inverse Problems in Partial Differential Equations. Springer, New York.
- 5. Kabanikhin, S. I. (2011). Inverse and Ill-posed Problems: Theory and Applications. Inverse and Ill-Posed Problems Series, Vol. 55. De Gruyter.
- 6. 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.
- 7. Kanca, F., Bağlan, I. (2018). Inverse problem for Euler–Bernoulli equation with periodic boundary condition. Filomat, 32(16), 5691–5705.
- 8. Mansur, I., Tekin, I. (2016). Inverse coefficient problems for a first order hyperbolic system. Applied Numerical Mathematics, 106, 98–115.
- 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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematiksel Yöntemler ve Özel Fonksiyonlar |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Gönderilme Tarihi | 9 Ekim 2025 |
| Kabul Tarihi | 24 Kasım 2025 |
| Yayımlanma Tarihi | 31 Aralık 2025 |
| DOI | https://doi.org/10.38061/idunas.1800322 |
| IZ | https://izlik.org/JA75NZ38FH |
| Yayımlandığı Sayı | Yıl 2025 Cilt: 8 Sayı: 2 |