SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 1

Study of 2m-th order parabolic equation in non-symmetric conical domains

Saida Cherfaoui(Université Houari Boumediene)0000-0001-8492-6262
Amor Kessab(Université Houari Boumediene)0000-0001-6742-2759
Arezki Kheloufi(Bejaia University)0000-0001-5584-1454
Pages
—
Publication Date
2020-02-06
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The analysis is performed in the framework of weighted anisotropic Sobolev spaces by using the domain decomposition method.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This article is devoted to the study of a $N$-space dimensional linear high-order parabolic equation, subject to Cauchy-Dirichlet boundary conditions.
📊
Key Findings & Data:The problem is set in a non-symmetric conical domain.
💡
Conclusion & Impact:The analysis is performed in the framework of weighted anisotropic Sobolev spaces by using the domain decomposition method.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:High-order parabolic equations · conical domains · anisotropic weighted Sobolev spaces

Abstract

This article is devoted to the study of a $N$-space dimensional linear high-order parabolic equation, subject to Cauchy-Dirichlet boundary conditions. The problem is set in a non-symmetric conical domain. The analysis is performed in the framework of weighted anisotropic Sobolev spaces by using the domain decomposition method.

🔖

Cite This Article

Cherfaoui, S., Kessab, A., Kheloufi, A. (2020). Study of 2m-th order parabolic equation in non-symmetric conical domains. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 1. https://doi.org/10.15672/hujms.546340

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (26)

  1. E.A. Baderko, The solvability of boundary value problems for higher order parabolic equations in domains with curvilinear lateral boundaries, Differ. Uravn. 10 (12), 1781– 1792, 1976.
  2. E.A. Baderko, On the solution of boundary value problems for linear parabolic equations of arbitrary order in noncylindrical domains by the method of boundary integral equations, PhD Thesis, Moscow, 1992.
  3. V. Besov, Continuation of functions from $L_p^l$ and $W_p^l$, Proc. Steklov Inst. Math. 89, 5–17, 1967.
  4. M.F. Cherepova, On the solvability of boundary value problems for a higher order parabolic equation with growing coefficients, Dokl. Math. 74 (3), 819–820 2006.
  5. S. Cherfaoui, A. Kessab, and A. Kheloufi, On 2m-th order parabolic equations with mixed boundary conditions in non-rectangular domains, Sib. Èlektron. Mat. Izv. 14, 73–91, 2017.
  6. V.A. Galaktionov, On regularity of a boundary point for higher-order parabolic equations: towards Petrovskii-type criterion by blow-up approach, Nonlinear Differ. Equ. Appl. 5 (16), 597–655, 2009.
  7. A. Grimaldi Piro and F. Ragnedda, Higher-order parabolic operators in domains with a "nonsmooth" boundary, Rend. Sem. Fac.Sci. Univ. Cagliari 54, 45–62, 1984.
  8. P. Grisvard and G. Looss, Problèmes aux limites unilatéraux dans des domaines non réguliers, Jour. Equ. Dériv. Part. 1–26, 1976.
  9. A. Kheloufi, Resolutions of parabolic equations in non-symmetric conical domains, Electron. J. Differ. Equ. 2012 (116), 1–14, 2012.
  10. A. Kheloufi, On a fourth order parabolic equation in a nonregular domain of $\mathbb{R}^3$, Mediterr. J. Math. 12, 803–820, 2015.
  11. A. Kheloufi, Study of a 2m-th order parabolic equation in a non-regular type of prism of $\mathbb{R}^{N+1}$, Georgian Math. J. 23 (2), 227–237, 2016.
  12. A. Kheloufi, On the Dirichlet problem for the heat equation in non-symmetric conical domains of $\mathbb{R}^{N+1}$, Palestine J. Math. 6 (1), 287–300, 2017.
  13. A. Kheloufi and B.K. Sadallah, On the regularity of the heat equation solution in noncylindrical domains: two approaches, Appl. Math. Comput. 218, 1623–1633, 2011.
  14. A. Kheloufi and B.K. Sadallah, Study of the heat equation in a symmetric conical type domain of $\mathbb{R}^{N+1}$, Math. Methods Appl. Sci. 37, 1807–1818, 2014.
  15. A. Kheloufi and B.K. Sadallah, Resolution of a high-order parabolic equation in conical time-dependent domains of $\mathbb{R}^{3}$, Arab J. Math. Sci. 22, 165–181, 2016.
  16. V.A. Kondrat’ev, Boundary problems for parabolic equations in closed regions, Am. Math. Soc. Providence. R I. 450–504, 1966.
  17. V.A. Kozlov, Coefficients in the asymptotic solutions of the Cauchy boundary-value parabolic problems in domains with a conical point, Siberian Math. J. 29, 222–233, 1988.
  18. R. Labbas and B.K. Sadallah, Smoothness of the solution of a fourth order parabolic equation in a polygonal domain, Int. J. Appl. Math. 1, 75–90, 1999.
  19. O.A. Ladyzhenskaya and V.A. Solonnikov and N.N. Ural’tseva, Linear and quasilinear equations of parabolic type, (A.M.S., Providence, Rhode Island, 1968).
  20. J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, 1, 2, Dunod, Paris, 1968.
  21. A. Maghnouji, Problèmes aux limites paraboliques dans un domaine non régulier, C.R.A.S. 316, 331–336, 1993.
  22. V.P. Mikhailov, The Dirichlet problem for a parabolic equation I, Mat. Sb. (N.S.) 61 (103), 40–64, 1963.
  23. V.P. Mikhailov, The Dirichlet problem for a parabolic equation II, Mat. Sb. (N.S.) 62 (104), 140–159, 1963.
  24. B.K. Sadallah, Etude d’un problème 2m-parabolique dans des domaines plan non rectangulaires, Boll. Un. Mat. Ital. 5 (2-B), 51–112, 1983.
  25. B.K. Sadallah, Singularities of the solution of a 2m-parabolic problem in a polygonal domain, Arab J. Math. Sci. 4 (2), 31–41, 1998.
  26. B.K. Sadallah, Study of a parabolic problem in a conical domain, Math. J. Okayama Univ. 56, 157–169, 2014.