TISH PROTEZLARI OSTIDAGI TOʻQIMALARDA SUYUQLIKLAR HARAKATINING STEFAN MODELI
##article.subject##:
protez stomatiti, Stefan modeli, erkin chegara, reaksiya–diffuziya–konveksiya, asimptotik baholar, protez–to‘qima interfeysi##article.abstract##
Maqolada protez–to‘qima tizimi uchun Stefan tipidagi erkin chegarali ikki fazali reaksiya–diffuziya–konveksiya modeli taklif etiladi. Modelning global klassik yechimi mavjudligi va yagonaligi hamda aprior va katta vaqtlar uchun asimptotik baholari asoslanadi. Interfeys () harakati Stefan sharti orqali aniqlanadi; soddalashtirilgan front-tracking sonli sxema yordamida protez–to‘qima interfeysi dinamikasi va bosim maydonlari ( , ) vizuallashtiriladi. Natijalar periferik ta’minot () mavjudida interfeysning chekkaga yopishmasligini va bosimlarning barqarorlashishini ko‘rsatadi. Klinik talqinda model protez stomatiti xavfini baholash va individual sozlashni rejalashda qo‘llanadi.
Библиографические ссылки
João Paulo Mendes Tribst, Gabriel Kalil Rocha Pereira, Cornelis Johannes Kleverlaan. Advancements in Dental Care: The Evolving Landscape of Prosthetic Dentistry. J Clin Med. 2024 Feb 21;13(5):1225. doi: 10.3390/jcm13051225
Tashpulatova K.M. Application of mathematical modeling in prosthetics on implants. World Bulletin of Public Health (WBPH), Volume-43, February 2025. 91-97.
Tashpulatova K.M. Safarov M.T. Ruzimbetov Kh.B. Sultanova Sh.H. Experience in the use of mathematical modeling to predict the long-term durability of prosthetics on dental implants. (application of mathematical modeling in prosthetics on implants.). Western European Journal of Modern Experiments and Scientific Methods. Volume 2, Issue 3, March 2024. 14-23.
Elmurodov A.N. and Rasulov M.S., On a Uniqueness of Solution for a Reaction-Diffusion Type System with a Free Boundary. Lobachevskii Journal of Mathematics. №43 (8), 2022. 2099-2106.
Friedman A. Free boundary problems in biology. Phil. Trans. R. Soc. A 373: 20140368. 2015. https://doi.org/10.1098/rsta.2014.0368
Friedman A. Free boundary problems in science and technology. Notices of the: AMS. V. 47, NUMBER 8. 854-861.
Liang R., Guo W., Qiao X., Wen H.,. Yu M, Tang W., Liu L., Wei Y., Tian W.. Biomechanical analysis and comparison of 12 dental implant systems using 3D finite element study. Comput methods biomech biomed engin. 18(12):1340-8. 2015. doi:10.1080/10255842.2014.903930
Grenoble D. E., Knoell A. C., Unified approach to the biomechanics of dental implantology. JPL Quarterly Technical Review. V. 2, Number 4. 1973.
Sinan Muftu. Biomechanical modeling of the mandible and teeth. The NIH/NIGMS Center for Integrative Biomedical Computing. https://www.sci.utah.edu/collaborations/97-muftu.html
Shaukat A., Zehra N., Kaleem M. and Fareed A. M.. Implant biomechanics relating to the dental implant and prosthesis design: In-vitro strain gauge analysis and finite element analysis. AIP Advances 14, 045134 (2024). https://doi.org/10.1063/5.0199243
Alemayehu Dawit Bogale, Todoh Masahiro and Huang Song-Jeng, Hybrid Biomechanical Design of Dental Implants: Integrating Solid and Gyroid Triply Periodic Minimal Surface Lattice Architectures for Optimized Stress Distribution. J. Funct. Biomater. 2025, 16(2), 54; https://doi.org/10.3390/jfb16020054
Prados-Privado M., Bea J.A. and Prados-Frutos J.C. Presentation of a Mathematical Model to Predict Long-term Behaviour of Implants and their Prosthesis based on Probabilistic Fatigue. Journal of Dentistry & Oral Disorders. 2017; 3(1): 1050.
Ryll A., Bucher J., Bonin A., Bongard S., Gonçalves E., Saez-Rodriguez J., Niklas J. and Klamt S.. A model integration approach linking signalling and gene-regulatory logic with kinetic metabolic models. PMID: 25063553. DOI: 10.1016/j.biosystems.2014.07.002
Riznichenko G. Y.. Mathematical models in Biophysics. https://www.biophysics.org/Portals/0/BPSAssets/Articles/galina.pdf
Tadeusz K., Katarzyna D. L. Subdiffusive Reaction Front in the Enamel Caries Process. Diffusion Fundamentals 2. (2005) pp.1 – 2.
Lo Bianco S.G., La Manna D. A., Velichkov B. Free boundary cluster with robin condition on the transmission interface. 1991.
Avner Friedman, Bei Hu, Juan José L. Velazques, A Stefan problem for a protocell model with symmetry-breaking bifurcations of analytic solutions. Interfaces Free Bound. 3 (2001), no. 2, pp. 143–199. DOI 10.4171/IFB/37
Mimura M., A stefan-like problem in biology. 数理解析研究所講究録. 989 巻 1997 年 31-41.
Verigin N.N. Filtratsion jarayonlarning ikki fazali modellari. Neft-gaz geologiyasi. - 1978. - №5. - B. 67-73.
Wang L. Limitations of quasi-static approaches. Arch Oral Biol. 2020. Vol. 78. P. 112-120.
Asrakulova D. and Elmurodov A.N., A reaction-diffusion-advection competition model with a free boundary. Uzbek Mathematical Journal. №65(3), 2021. 25-37.
Chen X. F. and Friedman A., A free boundary problem arising in a model of wound healing, SIAM J. Math. Anal., №32, 2000, 778-800.
A.N. Elmurodov, Two-phase problem with a free boundary for systems of parabolic equations with a nonlinear term of convection. Vestnik KRAUNC. Fiziko-Matematicheskie Nauki, №36, (3) 2021. 110-122.
