Research Article
Fourier Analysis of Inverse Coefficient Nonlinear Hyperbolic Equations under Periodic Boundary Conditions
Abstract
Bu çalışma, periyodik sınır koşullarına sahip tek boyutlu ters katsayılı doğrusal olmayan hiperbolik denklemin analitik analizini sunar. Analitik çözüm, Fourier yöntemi uygulanarak türetilir. Yakınsamayı belirlemek ve doğrusal olmayan problemin çözümünün varlığını, benzersizliğini ve kararlılığını değerlendirmek için yinelemeli bir yaklaşım kullanılır.
References
- 1. Tekin, I. (2018). Existence and uniqueness of an inverse problem for a second order hyperbolic equation. Universal Journal of Mathematics and Applications, 1(3), 178-185. https://doi.org/10.32323/ujma.439662
- 2. 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.
- 3. Asanova, A., Dzhumabaev, D. (2004). Periodic solutions of systems of hyperbolic equations bounded on a plane. Ukrainian Mathematical Journal, 56(4), 682-694. https://doi.org/10.1007/s11253-005-0103-0
- 4. Huntul, M., Abbas, M., Băleanu, D. (2021). An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation. Advances in Difference Equations, 2021(1). https://doi.org/10.1186/s13662-021-03608-1
- 5. Denisov, A.M., Shirkova, E.Y. (2013). Inverse Problem for a Quasilinear Hyperbolic Equation with a Nonlocal Boundary Condition Containing a Delay Argument. Differ. Equations, 49, 1053–1061. doi: 10.1134/S0012266113090012
- 6. Mehraliyev, Y., Huntul, M., Ramazanova, A., Tamsir, M., & Emadifar, H. (2022). An inverse boundary value problem for transverse vibrations of a bar. Boundary Value Problems, 2022(1). https://doi.org/10.1186/s13661-022-01679-x
- 7. Kanca, F., Bağlan, İ. (2018). Inverse problem for Euler-Bernoulli equation with periodic boundary condition. Filomat, 32(16).
- 8. Bağlan, İ. (2019). Analysis of Two-Dimensional Non-Linear Burgers'equations. TWMS Journal of Applied and Engineering Mathematics, 9(1), 38-48.
- 9. Baglan, I. (2015). Determination of a Coefficient in a Quasilinear Parabolic Equation with Periodic Boundary Condition. Inverse Prob. Sci. Eng., 23, 884–900. doi: 10.1080/17415977.2014.947479
Fourier Analysis of Inverse Coefficient Nonlinear Hyperbolic Equations under Periodic Boundary Conditions
Abstract
This study presents an analytical analysis of a one-dimensional inverse coefficient nonlinear hyperbolic equation with periodic boundary conditions. The analytical solution is derived by applying Fourier method. An iterative approach is used to establish convergence and to assess the existence, uniqueness and stability of the solution to the nonlinear problem.
References
- 1. Tekin, I. (2018). Existence and uniqueness of an inverse problem for a second order hyperbolic equation. Universal Journal of Mathematics and Applications, 1(3), 178-185. https://doi.org/10.32323/ujma.439662
- 2. 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.
- 3. Asanova, A., Dzhumabaev, D. (2004). Periodic solutions of systems of hyperbolic equations bounded on a plane. Ukrainian Mathematical Journal, 56(4), 682-694. https://doi.org/10.1007/s11253-005-0103-0
- 4. Huntul, M., Abbas, M., Băleanu, D. (2021). An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation. Advances in Difference Equations, 2021(1). https://doi.org/10.1186/s13662-021-03608-1
- 5. Denisov, A.M., Shirkova, E.Y. (2013). Inverse Problem for a Quasilinear Hyperbolic Equation with a Nonlocal Boundary Condition Containing a Delay Argument. Differ. Equations, 49, 1053–1061. doi: 10.1134/S0012266113090012
- 6. Mehraliyev, Y., Huntul, M., Ramazanova, A., Tamsir, M., & Emadifar, H. (2022). An inverse boundary value problem for transverse vibrations of a bar. Boundary Value Problems, 2022(1). https://doi.org/10.1186/s13661-022-01679-x
- 7. Kanca, F., Bağlan, İ. (2018). Inverse problem for Euler-Bernoulli equation with periodic boundary condition. Filomat, 32(16).
- 8. Bağlan, İ. (2019). Analysis of Two-Dimensional Non-Linear Burgers'equations. TWMS Journal of Applied and Engineering Mathematics, 9(1), 38-48.
- 9. Baglan, I. (2015). Determination of a Coefficient in a Quasilinear Parabolic Equation with Periodic Boundary Condition. Inverse Prob. Sci. Eng., 23, 884–900. doi: 10.1080/17415977.2014.947479
There are 9 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Applied Mathematics (Other) |
| Journal Section | Articles |
| Authors | |
| Publication Date | December 27, 2024 |
| Submission Date | November 22, 2024 |
| Acceptance Date | December 9, 2024 |
| Published in Issue | Year 2024 Volume: 7 Issue: 2 |
