Araştırma Makalesi
Yıl 2024,
, 130 - 134, 28.03.2024
Öz
Kaynakça
- [1] Payne L.E., Improperly Posed Problems in Partial Differential Equations. 1st ed. Philadelphia: Society for Industrial and Applied Mathematics, (1975) 19-42.
- [2] Isakov V., Inverse Problems for Partial Differential Equations. 2nd ed. New York: Springer, (2006) 89-295.
- [3] Kabanikhin S.I., Definitions and Examples of Inverse and Ill-Posed Problems, J. Inverse Ill-Pose. Probl., 16 (4) (2008) 317-357.
- [4] Klibanov M.V., Timonov A.A., Carleman Estimates for Coefficient Inverse Problems and Numerical Applications. 1st ed. The Netherlands: VSP, (2004) 79-145.
- [5] Lavrent’ev M.M., Romanov V.G., Shishatskii S.P., Ill-Posed Problems of Mathematical Physics and Analysis. 1st ed. Providence: American Mathematical Society, (1986) 7-261.
- [6] Amirov A., Gölgeleyen F., Solvability of an Inverse Problem for the Kinetic Equation and a Symbolic Algorithm, Comput. Model. Eng. Sci., 65 (2) (2010) 179-191.
- [7] Bellassoued M., Yamamoto M., Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems. 1st ed. Tokyo: Springer, (2017) 63-239.
- [8] Gölgeleyen F., Yamamoto M., Uniqueness of Solution of an Inverse Source Problem for Ultrahyperbolic Equations, Inverse Probl., 36 (3) (2020) 035008.
- [9] Gölgeleyen İ., Kaytmaz Ö., Uniqueness for a Cauchy Problem for the Generalized Schrödinger Equation, AIMS Math., 8 (3) (2023) 5703-5724.
- [10] Gölgeleyen İ., Yıldız M., On the Solution an Ill-Posed Boundary Value Problem for Second-Order Evolution Equations, Cumhuriyet Sci. J., 40 (1) (2019) 173-178.
Yıl 2024,
, 130 - 134, 28.03.2024
Öz
In this study, we consider an inverse problem of determining an unknown source function in the right-hand side of an elliptic equation which is ill-posed in the Hadamard sense. To investigate the solvability of the problem, we reduce it to a Dirichlet problem for a third-order partial differential equation with homogeneous boundary condition. Since the problem is linear, the proof of the uniqueness theorem is based on the Fredholm Alternative Theorem. We prove the existence of the solution to the problem by using the Galerkin method.
Anahtar Kelimeler
Kaynakça
- [1] Payne L.E., Improperly Posed Problems in Partial Differential Equations. 1st ed. Philadelphia: Society for Industrial and Applied Mathematics, (1975) 19-42.
- [2] Isakov V., Inverse Problems for Partial Differential Equations. 2nd ed. New York: Springer, (2006) 89-295.
- [3] Kabanikhin S.I., Definitions and Examples of Inverse and Ill-Posed Problems, J. Inverse Ill-Pose. Probl., 16 (4) (2008) 317-357.
- [4] Klibanov M.V., Timonov A.A., Carleman Estimates for Coefficient Inverse Problems and Numerical Applications. 1st ed. The Netherlands: VSP, (2004) 79-145.
- [5] Lavrent’ev M.M., Romanov V.G., Shishatskii S.P., Ill-Posed Problems of Mathematical Physics and Analysis. 1st ed. Providence: American Mathematical Society, (1986) 7-261.
- [6] Amirov A., Gölgeleyen F., Solvability of an Inverse Problem for the Kinetic Equation and a Symbolic Algorithm, Comput. Model. Eng. Sci., 65 (2) (2010) 179-191.
- [7] Bellassoued M., Yamamoto M., Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems. 1st ed. Tokyo: Springer, (2017) 63-239.
- [8] Gölgeleyen F., Yamamoto M., Uniqueness of Solution of an Inverse Source Problem for Ultrahyperbolic Equations, Inverse Probl., 36 (3) (2020) 035008.
- [9] Gölgeleyen İ., Kaytmaz Ö., Uniqueness for a Cauchy Problem for the Generalized Schrödinger Equation, AIMS Math., 8 (3) (2023) 5703-5724.
- [10] Gölgeleyen İ., Yıldız M., On the Solution an Ill-Posed Boundary Value Problem for Second-Order Evolution Equations, Cumhuriyet Sci. J., 40 (1) (2019) 173-178.
Toplam 10 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Uygulamalı Matematik (Diğer) |
| Bölüm | Natural Sciences |
| Yazarlar | |
| Yayımlanma Tarihi | 28 Mart 2024 |
| Gönderilme Tarihi | 13 Eylül 2023 |
| Kabul Tarihi | 26 Şubat 2024 |
| Yayımlandığı Sayı | Yıl 2024 |