Inhomogeneous Problem for Quasi-Stationary Equations of Complex Heat Transfer with Reflection and Refraction Conditions

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Abstract

The paper considers an inhomogeneous initial-boundary value problem for a nonlinear parabolic-elliptic system simulating radiative heat transfer with Fresnel matching conditions on the surfaces of discontinuity of the refractive index. Nonlocal-in-time unique solvability of the problem is proved.

About the authors

A. Yu. Chebotarev

Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences

Author for correspondence.
Email: cheb@iam.dvo.ru
690041, Vladivostok, Russia

References

  1. Ковтанюк А.Е., Гренкин Г.В., Чеботарев А.Ю. Использование диффузионного приближения для моделирования радиационных и тепловых процессов в кожном покрове // Оптика и спектроскопия. 2017. Т. 123. № 2. С. 194–199.
  2. Chebotarev A.Y., Grenkin G.V., Kovtanyuk A.E., Botkin N.D., Hoffmann K.-H. Diffusion approximation of the radiative-conductive heat transfer model with Fresnel matching conditions// Communications in Nonlinear Science and Numerical Simulation. 2018. № 57. C. 290–298.
  3. Чеботарев А.Ю. Неоднородная краевая задача для уравнений сложного теплообмена с френелевскими условиями сопряжения // Дифференц. ур-ния. 2020. Т. 56. № 12. С. 1660–1665.
  4. Chebotarev A.Y., Kovtanyuk A.E. Quasi-static diffusion model of complex heat transfer with reflection and refraction conditions // J. Math. Anal. Appl. 2022. V. 507. 125745.
  5. Pinnau R. Analysis of optimal boundary control for radiative heat transfer modeled by -system // Commun. Math. Sci. 2007. V. 5. № 4. P. 951–969.
  6. Ковтанюк А.Е., Чеботарев А.Ю. Стационарная задача сложного теплообмена // Ж. вычисл. матем. и матем. физ. 2014. Т. 54. № 4. С. 711–719.
  7. Kovtanyuk A.E., Chebotarev A.Yu., Botkin N.D., Hoffmann K.-H. Theoretical analysis of an optimal control problem of conductive-convective-radiative heat transfer // J. Math. Anal. Appl. 2014. V. 412. № 1. P. 520–528.
  8. Гренкин Г.В., Чеботарев А.Ю. Нестационарная задача сложного теплообмена // Ж. вычисл. матем. и матем. физ. 2014. Т. 54. № 11. С. 1806–1816.
  9. Kovtanyuk A.E., Chebotarev A.Yu., Botkin N.D., Hoffmann K.-H. Unique solvability of a steady-state complex heat transfer model // Commun. Nonlinear Sci. Numer. Simul. 2015. V. 20. № 3. P. 776–784.
  10. Chebotarev A.Yu., Kovtanyuk A.E., Grenkin G.V., Botkin N.D., Hoffmann K.-H. Nondegeneracy of optimality conditions in control problems for a radiative-conductive heat transfer model // Appl. Math. Comput. 2016. V. 289. P. 371–380.
  11. Grenkin G.V., Chebotarev A.Yu., Kovtanyuk A.E., Botkin N.D., Hoffmann K.-H. Boundary optimal control problem of complex heat transfer model // J. Math. Anal. Appl. 2016. V. 433. № 2. P. 1243–1260.
  12. Chebotarev A.Yu., Grenkin G.V., Kovtanyuk A.E. Inhomogeneous steady-state problem of complex heat transfer // ESAIM Math. Model. Numer. Anal. 2017. V. 51. № 6. P. 2511–2519.
  13. Chebotarev A.Yu., Grenkin G.V., Kovtanyuk A.E., Botkin N.D., Hoffmann K.-H. Inverse problem with finite overdetermination for steady-state equations of radiative heat exchange // J. Math. Anal. Appl. 2018. V. 460. № 2. P. 737–744.
  14. Chebotarev A.Yu., Pinnau R. An inverse problem for a quasi-static approximate model of radiative heat transfer // J. Math. Anal. Appl. 2019. V. 472. № 1. P. 314–327.
  15. Amosov A. Unique Solvability of a Nonstationary Problem of Radiative - Conductive Heat Exchange in a System of Semitransparent Bodies // Russian J. of Math. Phys. 2016. V. 23. № 3. P. 309–334.
  16. Amosov A.A. Unique Solvability of Stationary Radiative – Conductive Heat Transfer Problem in a System of Semitransparent Bodies // J. of Math. Sc. 2017. V. 224. № 5. P. 618–646.
  17. Amosov A.A. Nonstationary problem of complex heat transfer in a system of semitransparent bodies with boundary-value conditions of diffuse reflection and refraction of radiation // J. Math. Sci. 2018. V. 233. № 6. P. 777–806.
  18. Amosov A.A., Krymov N.E. On a Nonstandard Boundary Value Problem Arising in Homogenization of Complex Heat Transfer Problems // J. of Math. Sc. 2020. V. 244. P. 357–377.
  19. Amosov A.A. Asymptotic Behavior of a Solution to the Radiative Transfer Equation in a Multilayered Medium with Diffuse Reflection and Refraction Conditions // J Math Sci. 2020. V. 244. P. 541–575.
  20. Amosov A. Unique solvability of a stationary radiative-conductive heat transfer problem in a system consisting of an absolutely black body and several semitransparent bodies // Mathematical Methods in the Applied Sciences. 2021. V. 44. № 13. P. 10703–10733.
  21. Amosov A. Unique solvability of a stationary radiative-conductive heat transfer problem in a semitransparent body with absolutely black inclusions // Z. Angew. Math. Phys. 2021. V. 72. Article number:104.
  22. Amosov A.A. Unique solvability of the stationary complex heat transfer problem in a system of gray bodies with semitransparent inclusions // J. Math. Sci. (United States). 2021. V. 255. Issue 4. P. 353–388.
  23. Amosov A. Nonstationary Radiative-Conductive Heat Transfer Problem in a Semitransparent Body with Absolutely Black Inclusions // Mathematics. 2021. V. 9. № 13. P. 1471.
  24. Темам Р. Уравнения Навье–Стокса. Теория и численный анализ. М.: Мир, 1981.

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