
تعداد نشریات | 21 |
تعداد شمارهها | 610 |
تعداد مقالات | 9,028 |
تعداد مشاهده مقاله | 67,082,851 |
تعداد دریافت فایل اصل مقاله | 7,656,345 |
An inverse problem for homogeneous time-fractional diffusion problem on the sphere | ||
International Journal of Nonlinear Analysis and Applications | ||
دوره 12، Special Issue، اسفند 2021، صفحه 653-662 اصل مقاله (345.13 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.5402 | ||
نویسنده | ||
Danh Hua Quoc Nam* | ||
Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam | ||
تاریخ دریافت: 07 خرداد 1399، تاریخ بازنگری: 19 مرداد 1399، تاریخ پذیرش: 30 مرداد 1399 | ||
چکیده | ||
In this paper, we consider an inverse problem for the time-fractional diffusion equation on the sphere where the final data on the sphere are given. The problem is ill-posed in the sense of Hadamard. Hence, the regularization method has to be used for the stable approximate solution. Then the well-posedness of the proposed regularizing problem and convergence property of the regularizing solution to the exact one is proved. Error estimates for this method are provided together with a selection rule for the regularization parameter. | ||
کلیدواژهها | ||
Time fractional diffusion؛ inverse problem, Ill-posed problem؛ Convergence estimates | ||
مراجع | ||
[1] E. Abdolmaleki, H. Saberi Najafi, Analytical Solution for the Time Fractional Newell-Whitehead-Segel Equation by Using Modified Residual Power Series Method, International Journal of Nonlinear Analysis and Applications 10(Special Issue (Nonlinear Analysis in Engineering and Sciences)) (2019) 155–167. [2] M. Badr, A. Yazdani, H. Jafari, Stability of a finite volume element method for the time-fractional advectiondiffusion equation, Numerical Methods for Partial Differential Equations 34(5) (2018) 1459–1471. [3] N. Faraz, Y. Khan, H. Jafari, A. Yildirim, M. Madani, Fractional variational iteration method via modified Riemann–Liouville derivative, Journal of King Saud University-Science 23(4) (2011) 413–417. [4] H. Jafari, H. Tajadodi, New method for solving a class of fractional partial differential equations with applications, Thermal Science 22(Supplement 1) (2018) 277–286. [5] D. Kumar, J. Singh, D. Baleanu, A new analysis for fractional model of regularized long-wave equation arising in ion acoustic plasma waves, Mathematical Methods in the Applied Sciences 40(15) (2017) 5642–5653. [6] L.D. Long, Y. Zhou, T.T. Binh, N. Can, A Mollification Regularization Method for the Inverse Source Problem for a Time Fractional Diffusion Equation, Mathematics 7(11) (2019) 1048. [7] N.H. Luc, D. Baleanu, N.H. Can, Reconstructing the right-hand side of a fractional subdiffusion equation from the final data, Journal of Inequalities and Applications 1 (2020) 1–15. [8] W. McLean, Regularity of solutions to a time-fractional diffusion equation, ANZIAM J. 52(2) (2010) 123–138. [9] I. Podlubny, Fractional differential equations, Academic Press, London, 1999. [10] S.S. Roshan, H. Jafari, D. Baleanu, Solving FDEs with Caputo-Fabrizio derivative by operational matrix based on Genocchi polynomials, Mathematical Methods in the Applied Sciences 41(18) (2018) 9134–9141. [11] K. Sakamoto, M. Yamamoto, Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems, J. Math. Anal. Appl. 382(1) (2011) 426–447 [12] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional integrals and derivatives: Theory and Applications, Gordon and Breach Science Publishers, Nauka i Tekhnika, Minsk, 1987. [13] M. Soluki, S. Rasouli, G. Afrouzi, On a class of nonlinear fractional Schr¨odinger-Poisson systems, International Journal of Nonlinear Analysis and Applications 10(Special Issue (Nonlinear Analysis in Engineering and Sciences)) (2019) 123–132. [14] Q.T. Le Gia Approximation of parabolic PDEs on spheres using collocation method, Adv. Comput. Math. 22(4) (2005) 377–397. [15] Q.T. L. Gia, N.H. Tuan, T. Tran, Solving the backward heat equation on the unit sphere, ANZIAM J. 56 (2016) 262–278. [16] D.D. Trong, N.H. Tuan, A nonhomogeneous backward heat problem: Regularization and error estimates, Electronic Journal of Differential Equations (EJDE)[electronic only], 2008(33) (2008) 1–14. [17] D.D. Trong, N.H. Tuan, P.H. Quan, A quasi-boundary value method for regularizing nonlinear ill-posed problems, Electronic Journal of Differential Equations (EJDE)[electronic only], 2009(109) (2009) 1–16. [18] N.H. Tuan, L.D. Long, S. Tatar, Tikhonov regularization method for a backward problem for the inhomogeneous time-fractional diffusion equation, Appl. Anal. 97(5) (2018) 842–863. [19] N.H. Tuan, Y. Zhou, N.H. Can, Identifying inverse source for fractional diffusion equation with Riemann–Liouville derivative, Computational and Applied Mathematics 39(2) (2020) 1–16. [20] H. Zeidabadi, R. Pourgholi, S. Tabasi, Solving a nonlinear inverse system of Burgers equations, International Journal of Nonlinear Analysis and Applications 10(1) (2019) 35–54. | ||
آمار تعداد مشاهده مقاله: 44,040 تعداد دریافت فایل اصل مقاله: 404 |