SELF-SIMULAR SOLUTIONS FOR ONE CLASS OF PARABOLIC EQUATION WITH DEGENERATE COEFFICIENT

SELF-SIMULAR SOLUTIONS FOR ONE CLASS OF PARABOLIC EQUATION WITH DEGENERATE COEFFICIENT

Authors

  • Anvar Xasanov Institute of Mathematics
  • Sardor Rashidov Institute mathematic

DOI:

https://doi.org/10.52754/16948645_2023_2_147

Keywords:

Self-similar solutions, differential equations, second order partial derivatives, boundary value problems, self-similar solution, singular equations

Abstract

Self-similar solutions of second-order partial differential equations play an important role in the study of boundary value problems, and self-similar solutions of singular equations are expressed through special functions [1-7].

References

Г. И. Баренблатт. Подобие, Автомодельность, Промежуточная асимптотика. Теория и приложения к геофизической гидродинамике. Ленинград, Гидрометеоиздат, 1982, 255 стр.

О.А. Фроловская. Автомодельные решения нестационарных пограничных слоев. Прикладная механика и теоретическая физика. 2002. т.43,N 1, 65-70.

Ю.Ю. Тарасевич.Нахождение и визуализация автомодельных решений дифференциальных уравнений в частных производных средствами Maple. Методические рекомендации. Астрахань, 2010. 23 стр.

А.Д.Полянин, В.Ф.Зайцев. Справочник по нелинейным уравнениям математической физики: Точные решения. М: Физматлит, 2002, 432 с.

A. Hasanov and N. Djuraev. Exact Solutions of the Thin Beam with Degrading Hysteresis Behavior. Lobachevskii Journal of Mathematics, 2022, Vol. 43, No. 3, pp. 577–584.

A. Hasanov and M. Ruzhansky. Hypergeometric Expansions of Solutions of the Degenerating Model Parabolic Equations of the Third Order. Lobachevskii Journal of Mathematics, 2020, Vol. 41, No. 1, pp. 27–31. DOI: https://doi.org/10.1134/S1995080220010059

M. Ruzhansky and A. Hasanov. Self-similar Solutions of Some Model Degenerate Partial Differential Equations of the Second, Third and Fourth Order. Lobachevskii Journal of Mathematics, 2020, Vol. 41, No. 6, pp. 1103–1114. DOI: https://doi.org/10.1134/S1995080220060153

A. Erd´elyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions, Vol. 2, McGraw-Hill Book Company, New York, Toronto and London, 1953.

Published

2023-12-30

How to Cite

Xasanov, A., & Rashidov, S. (2023). SELF-SIMULAR SOLUTIONS FOR ONE CLASS OF PARABOLIC EQUATION WITH DEGENERATE COEFFICIENT: SELF-SIMULAR SOLUTIONS FOR ONE CLASS OF PARABOLIC EQUATION WITH DEGENERATE COEFFICIENT. Journal of Osh State University. Mathematics. Physics. Technical Sciences, (2(3), 147–149. https://doi.org/10.52754/16948645_2023_2_147