ВИЗНАЧЕННЯ КОЕФIЦIЄНТIВ ПЕРШОГО ПОРЯДКУ В РIВНЯННI ДИФУЗIЇ З ДРОБОВОЮ ПОХIДНОЮ ЗА ЧАСОМ
DOI: http://dx.doi.org/10.30970/vmm.2026.98.75-87
Анотація
Дослiджуємо обернену задачу про визначення класичного розв’язку першої крайової задачi для рiвняння дифузiї з дробовою похiдною за часом та залежних вiд часу неперервних коефiцiєнтiв при похiдних першого порядку у рiвняннi. Використовуємо iнтегральнi за просторовими змiнними умови перевизначення. Знаходимо достатнi умови єдиностi та локального за часом iснування класичного розв’язку оберненої задачi.
Ключовi слова: дробова похiдна, обернена задача, iнтегральна умова,
вектор-функцiя Грiна.
Повний текст:
PDF (English)Посилання
Anh V.V. and Leonenko N.N. Spectral analysis of fractional kinetic equations with random datas // J. of Statistical Physics. – 2001. – V. 104, no.5/6. – P. 1349-1387.
Eidelman S.D., Ivasyshen S.D., Kochubei A.N. Analytic methods in the theory of differential and pseudo-differential equations of parabolic type. – Birkhauser Verlag, Basel-Boston-Berlin, 2004.
Kochubei A. Fractional-parabolic systems // Potential Anal. – 2012. – V. 37. – P. 1–30. https://doi.org/10.1007/s11118-011-9243-z
Luchko Yu., Yamamoto M. General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems // Fract. Calc. Appl. Anal. – 2016. – V. 19. – P. 675-695.
Mainardi F. The fundamental solutions for the fractional diffusion-wave equation // Appl. Math. Lett. – 1996. – V. 9, no.6. – P. 23-28.
Matijchuk M.I. The connection between fundamental solutions of parabolic equations and fractional equations // Bukovinian Mathematical Journal. – 2016. – V. 4, no.3-4. – P. 101–114. (in Ukrainian)
Sakamoto K., Yamamoto M. Initial value/boundary-value problems for fractional diffusionwave equations and applications to some inverse problems // Journal of Mathematical Analises and Applications. – 2011. – V. 382, no.1. – P. 426–447.
Schneider W.R., and Wyss W. Fractional diffusion and wave equations // J. Math. Phys. – 1989. V. 30. – P. 134-144.
Janno J., Kasemets K. A positivitive principle for parbolic integro-differential equations and inverse problems with final overdetermination // Inverse Probl. Imaging. – 2009. – V. 3, no.1. – P. 17-41.
Janno J., Kinash N. Reconstruction of an order of derivative and a source term in a fractional diffusion equation from final measurements // Inverse Problems. – 2018. – V. 34, no.2, 025007.
Kirane M., Samet B., Torebek B. Determination of an unknown source term temperature distribution for the sub-diffusion equation at the initial and final data // Electron. J. Diff. Eqns. – 2017. – V. 2017, no.257.
Li Z., Yamamoto M. Inverse problems of determining coefficients of the fractional partial differential equations // ArXiv:1904.05505v1 [math.AP] 11 Apr 2019.
Yang F., Zhang Y., Li X.X. Landweber iterative method for identifying the initial value
problem of the time-space fraction diffusion-wave equation // Numer Algor. – 2019.
https://doi.org/10.1007/s11075-019-00734-6.
Y. Kian, L. Oksanen, E. Soccorsi, and M. Yamamoto, Global uniqueness in an inverse problem for timefractional diffusion equations // J. Diff. Equat. – 2018. – V. 264.
Aleroev T.S., Kirane M., Malik S.A. Determination of a source term for a time fractional diffusion equation with an integral type overdetermination condition // Electronic J. of Differential Equations. – 2013. – V. 2013, no.270. – P. 1-16, http://ejde.math.txstate.edu/2017/270.
El-Borai M.M. On the solvability of an inverse fractional abstract Cauchy problem //
LJRRAS. – 2001. – V. 4. – P. 411–415.
Ismailov M.I. Inverse source problem for a time-fractional diffusion equation with nonlocal boundary conditions // Applied Mathematical Modeling. – 2016. – V. 40, no.7/8. – P. 4891–4899.
Lopushansky A., Lopushansky O., Sharyn S. Nonlinear inverse problem of control diffusivity parameter determination for a space-time fractional diffusion equation // Appl. Math. Comput. – 2021. – V. 390, 125589. DOI 10.1016/j.amc.2020.125589.
Wei T. and Xian J. Determining a time-dependent coefficient in a time-fractional diffusion wave equation with the Caputo derivative by an additional integral condition // J. Comput. Appl. Math. – 2022. – V. 22, 404. – Paper No. 113910
Kirane M., Lopushansky A., Lopushanska H. Inverse problem to a fractional differential equation with a time and space-integral conditions // Math. Meth. Appl. Sci. – 2023. – V. 46, no.15. – P. 16381-16393. DOI10.1002/mma.9453.
Kirane M., Lopushansky A. and Lopushanska H. Determination of two unknown functions of different variables in a time-fractional differential equation // Math. Meth. Appl. Sci. – 2025. – V. 48, no. 4. – P. 4185-4194. DOI 10.1002/mma.10539.
Lopushanskyy A., Lopushanska H. Inverse problem with two unknown time-dependent functions for 2b-order differential equation with fractional derivative // Carpathian Math. Publ. – 2022. – V. 14, no.2. – P. 213-222. doi: 10.15330/cmp.14.1.213-222
Boyko P., Lopushansky A., Lopushanska H., Pukach P. Inverse initial problem for a timefractional diffusion-wave equation // Carpathian Math. Publ. – 2025. – V. 17, no.2. – P. 604-615. doi:10.15330/cmp.17.2.604-616
Посилання
- Поки немає зовнішніх посилань.