دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات43
تعداد شماره‌ها1,226
تعداد مقالات15,041
تعداد مشاهده مقاله50,585,461
تعداد دریافت فایل اصل مقاله13,674,874
Amini Sefidab, Behnam, Reihani, Parastoo. (1403). On a moving boundary problem associated with a mathematical model of breast cancer. سامانه مدیریت نشریات علمی, 12(1), 56-66. doi: 10.22034/cmde.2023.55447.2307
Behnam Amini Sefidab; Parastoo Reihani. "On a moving boundary problem associated with a mathematical model of breast cancer". سامانه مدیریت نشریات علمی, 12, 1, 1403, 56-66. doi: 10.22034/cmde.2023.55447.2307
Amini Sefidab, Behnam, Reihani, Parastoo. (1403). 'On a moving boundary problem associated with a mathematical model of breast cancer', سامانه مدیریت نشریات علمی, 12(1), pp. 56-66. doi: 10.22034/cmde.2023.55447.2307
Amini Sefidab, Behnam, Reihani, Parastoo. On a moving boundary problem associated with a mathematical model of breast cancer. سامانه مدیریت نشریات علمی, 1403; 12(1): 56-66. doi: 10.22034/cmde.2023.55447.2307

On a moving boundary problem associated with a mathematical model of breast cancer

Computational Methods for Differential Equations
مقاله 5، دوره 12، شماره 1، فروردین 2024، صفحه 56-66    اصل مقاله (523.16 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.55447.2307
نویسندگان
Behnam Amini Sefidab؛ Parastoo Reihani*
Department of Mathematics, Payame Noor University (PNU), P. O. Box: 19395-4697, Tehran, Iran.
چکیده
This paper is associated with a nonlinear parabolic moving boundary problem  raised from the mathematical modeling of the behavior of the breast avascular cancer tumors at their first stage. This model is a modification of the previous works. Using the weak form of the proposed problem, the uniqueness of the solution is proved. Based on the finite difference method, a variable time step approach is proposed to solve the problem, numerically. It is shown that the numerical approach preserves the positivity of the solution and is unconditionally stable. To show the robustness and ability of the numerical method, the numerical and exact solutions are discussed and compared for two examples with the exact solutions.
کلیدواژه‌ها
Moving boundary؛ Breast cancer؛ Uniqueness؛ Variable time step
مراجع
  • [1] K. Bao, An elementary mathematical modeling of drug resistance in cancer, Math. Biosci. Engin., 18(1) (2021), 339-353.
  • [2] S. Belkhir, F. Thomas, and B. Roche, Darwinian approaches for  cancer  treatment:  benefits  of  mathematical modeling, Cancers, 13(17) (2021), 4448.
  • [3] V. Bitsouni, V. Tsilidis, Mathematical modeling of tumor-immune system interactions: the effect of rituximab on breast cancer immune response, J. Theor. Bio., 539 (2022), 111001.
  • [4] E. Boghaert1, D. C. Radisky, C. M. Nelson, Lattice-based model of ductal carcinoma in situ suggests rules for breast cancer progression to an invasive state, PLOS Comput. Biol., 10 (2014), 1–14.
  • [5] S. J. Franks, H. M. Byrne, J. R. King, J. C. E. Underwood, C. E. Lewis, Modeling the early growth of ductal carcinoma in situ of the breast, J. Math. Biol., 47 (2003), 424–452.
  • [6] M. Garshasbi and M. Abdolmanafi, Identification of Some Unknown Parameters in an Aggressive-Invasive Cancer Model Using Adjoint Approach, Mediterr. J. Math. 16 (2019), 1-18.
  • [7] M. Garshasbi, Determination of unknown functions in a mathematical model of ductal carcinoma in situ, Numer. Meth. Part. Diff. Equ., 35(6) (2019), 2000-2016.
  • [8] M. Garshasbi and F. Sanaei, A variable time-step method for a space fractional diffusion moving boundary problem: An application to planar drug release devices, Int. J. Numer. Model., 34 (2021), e2852.
  • [9] M. Garshasbi and S. Malek Bagomghaleh, An iterative approach to solve a nonlinear moving boundary problem describing the solvent diffusion within glassy polymers, Math. Meth. Appl. Sci., 43 (2020), 3754–3772.
  • [10] M. Garshasbi and J. Sharafi, On the numerical solution of a class of variable coefficients parabolic moving boundary problems, J. Appl. Math. Comput., (2023).
  • [11] M. Garshasbi and S. Malek Bagomghaleh, On a moving boundary problem associated with the swelling drug release platforms, I. J. Comput. Math. 99(12) (2022), 2499-2523.
  • [12] L. Heng, Some problems arising from mathematical model of ductal carcinoma in situ, Electronic Theses and Dissertations, Paper 2789, (2017).
  • [13] K. Liu, Y. Xu, and D. Xu, Numerical algorithms for a free boundary problem model of DCIS and a related inverse problem, Applic. Anal., 99(7) (2018), 1181-1194.
  • [14] M. A. Ramadan and M. M. A. Murad, Inverse Nonnegativity of Tridiagonal M-Matrices under Diagonal Element- Wise Perturbation, Adv. Lin. Alg. & Mat. Theo., 5 (2015), 37-45.
  • [15] P. Reihani, H. Esmailpour, and F. Soltanian, An ABC algorithm based approach to solve a nonlinear inverse reaction-diffusion problem associate with the ecological invasions, Comput. Meth. Diff. Equ., 11 (2023), 143-160.
  • [16] S. Tabassum, N. B. Rosli, and M. S. A. B. Mazalan, Mathematical modeling of cancer growth process: a review, J. Phys.: Conference Series, IOP Publishing, 1366(1) (2019), 012018.
  • [17] N. T. Van Ravesteyn, J. J. Van Den Broek, X. Li, and S. J. Lee, Modeling ductal carcinoma in situ (DCIS): an overview of CISNET model approaches, Medical Decision Making, 38 (2018), 126S-139S.
  • [18] Y. Xu, An inverse problem for the free boundary model of ductal carcinoma in situ, More Progr. in Anal., World Science Publisher, (2008), 1429-1438.
  • [19] Y. Xu and R. Gilbert, Some inverse problems raised from  a mathematical model of ductal carcinoma in situ,  Math. Comput. Model., 49 (2009), 814–828.
  • [20] J. Zhou, Y. Xu, and H. Li, Another way of solving a free boundary problem related to DCIS model, Applic. Anal., 100(15) (2021).
آمار
تعداد مشاهده مقاله: 127
تعداد دریافت فایل اصل مقاله: 367


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب