Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition

Yıl: 2022 Cilt: 46 Sayı: 6 Sayfa Aralığı: 2430 - 2439 Metin Dili: İngilizce DOI: 10.55730/1300-0098.3278 İndeks Tarihi: 09-12-2022

Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition

Öz:
In this paper, the Dirac type integro differential system with a nonlocal integral boundary condition is considered. First, we derive the asymptotic expressions for the solutions and large eigenvalues. Second, we provide asymptotic expressions for the nodal points and prove that a dense subset of nodal points uniquely determines the boundary condition parameter and the potential function of the considered differential system. We also provide an effective procedure for solving the inverse nodal problem.
Anahtar Kelime: Dirac operator intego-differential operators inverse nodal problems nonlocal boundary conditions boundary value problem

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Bitsadze AV, Samarskii AA. Some elementary generalizations of linear elliptic boundary value problems. Doklady Akademii Nauk SSSR 1969; 185: 739-740.
  • [2] Day WA. Extensions of a property of the heat equation to linear thermoelasticity and order theories. Quarterly of Applied Mathematics 1982; 40: 319-330.
  • [3] Gordeziani N. On some nonlocal problems of the theory of elasticity. Bulletin of TICMI 2000; 4: 43-46.
  • [4] Yin YF. On nonlinear parabolic equations with nonlocal boundary conditions. Journal of Mathematical Analysis and Applications 1994; 185: 161-174. doi: doi.org/10.1006/jmaa.1994.1239
  • [5] Nakhushev AM. Equations of mathematical biology. Moscow: Vysshaya Shkola, 1995 (in Russian).
  • [6] Schuegerl K. Bioreaction Engineering. Reactions involving microorganisms and cells. vol. 1, John Wiley and Sons, 1987.
  • [7] Albeverio S, Hryniv R, Nizhnik LP. Inverse spectral problems for nonlocal Sturm-Liouville operators. Inverse Problems 2007; 23: 523-535. doi: doi.org/10.1088/0266-5611/23/2/005
  • [8] Freiling G, Yurko VA. Inverse problems for differential operators with a constant delay. Applied Mathematics Letters 2012; 25: 1999–2004. doi: 10.1016/j.aml.2012.03.026
  • [9] Kravchenko KV. On differential operators with nonlocal boundary conditions. Differentsialnye Uravneniya 2000; 36: 464–469. (English transl. in Differential Equations 2000; 3: 517–523).
  • [10] Nizhnik LP. Inverse nonlocal Sturm–Liouville problem. Inverse Problems 2010; 26: 125006. doi: 10.1088/0266- 5611/26/12/125006
  • [11] Bondarenko NP. An inverse problem for an integro-differential operator on a star-shaped graph. Mathematical Methods in the Applied Sciences 2018; 41: 1697-1702. doi: 10.1002/mma.4698
  • [12] Bondarenko NP. An inverse problem for the integro-differential Dirac system with partial information given on the convolution kernel. Journal of Inverse and Ill-posed Problems 2019; 27 (2): 151-157. 10.1515/jiip-2017-0058
  • [13] Bondarenko NP, Buterin SA. An inverse spectral problem for integro-differential Dirac operators with general convolution kernels. Applicable Analysis 2020; 99: 700-716.
  • [14] Bažant ZP, Jirásek M. Nonlocal integral formulation of plasticity and damage: survey of progress, american society of civil engineers. Journal of Engineering Mechanics 2002; 1119-1149.
  • [15] Buterin SA, Shieh CT. Inverse nodal problem for differential pencils. Applied Mathematics Letters 2009; 22: 1240- 1247.
  • [16] Buterin SA, On an inverse spectral problem for a convolution integro-differential operator. Results in Mathematics 2007; 50: 173-181.
  • [17] Buterin SA, Yurko VA. Inverse problems for second order integral and integro-differential operators. Analysis and Mathematical Physics 2018; 4: 1-10.
  • [18] Cheng YH, Law CK, Tsay J. Remarks on a new inverse nodal problem. Journal of Mathematical Analysis and Applications 2000; 248: 145-155.
  • [19] Çakmak Y. Inverse nodal problem for a conformable fractional diffusion operator. Inverse Problems in Science and Engineering 2021; 29 (9): 1308-1322. doi: 10.1080/17415977.2020.1847103
  • [20] Freiling G, Yurko VA. Inverse Sturm-Liouville problems and their applications. New York: Nova Science, 2001.
  • [21] Guo Y, Wei Y. Inverse nodal problem for Dirac equations with boundary conditions polynomially dependent on the spectral parameter. Results in Mathematics 2015; 67: 95-110.
  • [22] Guo Y, Wei Y, Yao R. Uniqueness theorems for the Dirac operator with eigenparameter boundary conditions and transmission conditions. Applicable Analysis 2020; 99 (9): 1564-1578. doi: 10.1080/00036811.2018.1540039
  • [23] Hald OH, McLaughlin JR. Solutions of inverse nodal problems. Inverse Problems 1989; 5: 307-347.
  • [24] Hu YT, Bondarenko NP, Shieh CT, Yang CF. Traces and inverse nodal problems for Dirac-type integro-differential operators on a graph. Applied Mathematics and Computation 2019; 363: 124606. doi: 10.1016/j.amc.2019.124606
  • [25] Keskin B. Inverse problems for one dimentional conformable fractional Dirac type integro differential system. Inverse Problems 2020; 363: 065001. doi: 10.1088/1361-6420/ab7e03
  • [26] Keskin B, Ozkan AS. Inverse nodal problems for Dirac-type integro-differential operators. Journal of Differential Equations 2017: 263: 8838-8847. doi: 10.1016/j.jde.2017.08.068
  • [27] Keskin B, Tel HD. Reconstruction of the Dirac-type integro-differential operator from nodal data. Numerical Functional Analysis and Optimization 2018; 39: 1208-1220. doi: 10.1080/01630563.2018.1470097
  • [28] Keskin B, Tel HD. Inverse nodal problems for Dirac-type integro-differential system with boundary conditions polynomially dependent on the spectral parameter. Cumhuriyet Science Journal 2019; 40 (4): 875-885. doi: 10.17776/csj.620668
  • [29] Kuryshova YV, Shieh CT. An Inverse nodal problem for integro-differential operators. Journal of Inverse and III-posed Problems 2010; 18: 357-369.
  • [30] Kuryshova YV. Inverse spectral problem for integro-differential operators. Mathematical Notes 2007; 81 (6): 767- 777.
  • [31] McLaughlin JR. Inverse spectral theory using nodal points as data – a uniqueness result. Journal of Differential Equations 1988; 73: 354-362.
  • [32] Lakshmikantham V, Rama Mi Mohana R. Theory of integro-differential equations Stability and Control: Theory, Methods and Applications. v.1, Singapore: Gordon and Breach Science Publishers, 1995.
  • [33] Law CK, Shen CL, Yang, CF. The Inverse nodal problem on the smoothness of the potential function. Inverse Problems 1999; 15 (1): 253-263. (Erratum, Inverse Problems 2001; 17: 361-363).
  • [34] Şen E. Traces and inverse nodal problems for a class of delay Sturm–Liouville operators. Turkish Journal of Mathematics 2021; 45: 305-318. doi: 10.3906/mat-2005-55
  • [35] Qin X, Gao Y, Yang C. Inverse nodal problems for the Sturm-Liouville Operator with some nonlocal integral conditions. Journal of Applied Mathematics and Physics 2019; 7: 111-122.
  • [36] Wang YP, Koyunbakan H, Yang CF. Trace formula for integro-differential operators on the finite interval. Acta Mathematicae Applicatae Sinica 2017; 33 (1): 141-146. doi: 10.1007/s10255-017-0644-7
  • [37] Yurko VA. An inverse problem for integro-differential operators. Matematicheskie Zametki 1991; 50: 134- 146.(English transl. in Mathematical Notes 1991; 50: 1188-1197).
  • [38] Shieh CT, Yurko VA. Inverse nodal and inverse spectral problems for discontinuous boundary value problems. Journal of Mathematical Analysis and Applications 2008; 347: 266-272. doi: 10.1016/j.jmaa.2008.05.097
  • [39] Yang XF. A solution of the nodal problem. Inverse Problems 1997; 13: 203-213.
  • [40] Yang CF. Inverse nodal problem for a class of nonlocal Sturm-Liouville operator. Mathematical Modelling and Analysis 2010; 15 (3): 383-392. doi: 10.3846/1392-6292.2010.15.383-392
  • [41] Yang CF. Trace and inverse problem of a discontinuous Sturm-Liouville operator with retarded argument. Journal of Mathematical Analysis and Applications 2012; 395: 30-41.
  • [42] Yang CF, Yurko VA. Recovering Dirac operator with nonlocal boundary conditions. Journal of Mathematical Analysis and Applications 2016; 440: 155-166.
  • [43] Yang CF, Huang ZY. Reconstruction of the Dirac operator from nodal data. Integral Equation and Operator Theory 2010; 66: 539-551. doi:10.1007/s00020-010-1763-1
  • [44] Yang CF, Pivovarchik VN. Inverse nodal problem for Dirac system with spectral parameter in boundary conditions. Complex Analysis and Operator Theory 2013; 7: 1211-1230. doi: 10.1007/s11785-011-0202-x
  • [45] Yilmaz E, Koyunbakan H. On the Lipschitz stability of inverse nodal problem for Dirac system. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 2021; 70 (1): 341-356. doi: 10.31801/cfsuasmas.733215
  • [46] Yılmaz E. Inverse nodal problem for an integro-differential operator. Cankaya University Journal of Science and Engineering 2015; 12 (1): 014-019.
APA Keskin B (2022). Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition. , 2430 - 2439. 10.55730/1300-0098.3278
Chicago Keskin Baki Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition. (2022): 2430 - 2439. 10.55730/1300-0098.3278
MLA Keskin Baki Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition. , 2022, ss.2430 - 2439. 10.55730/1300-0098.3278
AMA Keskin B Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition. . 2022; 2430 - 2439. 10.55730/1300-0098.3278
Vancouver Keskin B Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition. . 2022; 2430 - 2439. 10.55730/1300-0098.3278
IEEE Keskin B "Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition." , ss.2430 - 2439, 2022. 10.55730/1300-0098.3278
ISNAD Keskin, Baki. "Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition". (2022), 2430-2439. https://doi.org/10.55730/1300-0098.3278
APA Keskin B (2022). Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition. Turkish Journal of Mathematics, 46(6), 2430 - 2439. 10.55730/1300-0098.3278
Chicago Keskin Baki Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition. Turkish Journal of Mathematics 46, no.6 (2022): 2430 - 2439. 10.55730/1300-0098.3278
MLA Keskin Baki Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition. Turkish Journal of Mathematics, vol.46, no.6, 2022, ss.2430 - 2439. 10.55730/1300-0098.3278
AMA Keskin B Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition. Turkish Journal of Mathematics. 2022; 46(6): 2430 - 2439. 10.55730/1300-0098.3278
Vancouver Keskin B Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition. Turkish Journal of Mathematics. 2022; 46(6): 2430 - 2439. 10.55730/1300-0098.3278
IEEE Keskin B "Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition." Turkish Journal of Mathematics, 46, ss.2430 - 2439, 2022. 10.55730/1300-0098.3278
ISNAD Keskin, Baki. "Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition". Turkish Journal of Mathematics 46/6 (2022), 2430-2439. https://doi.org/10.55730/1300-0098.3278