Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 1

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

Sayfa
180–194
Yayın Tarihi
2020-02-06
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez:This article is devoted to the study of a $N$-space dimensional linear high-order parabolic equation, subject to Cauchy-Dirichlet boundary conditions.
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Temel Bulgular & Veri:The problem is set in a non-symmetric conical domain.
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Sonuç & Katkı:The analysis is performed in the framework of weighted anisotropic Sobolev spaces by using the domain decomposition method.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.

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Bu Makaleye Atıf Yap

CHERFAOUİ, S., KESSAB, A., KHELOUFİ, A. (2020). Study of 2m-th order parabolic equation in non-symmetric conical domains. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 180–194. https://ajindex.com/articles/669305

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Kaynakça (16)

  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 paraboli