Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 49 Sayı: 1, 180 - 194, 06.02.2020
https://doi.org/10.15672/hujms.546340

Öz

Kaynakça

  • [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.

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

Yıl 2020, Cilt: 49 Sayı: 1, 180 - 194, 06.02.2020
https://doi.org/10.15672/hujms.546340

Öz

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.

Kaynakça

  • [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.
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Saida Cherfaoui Bu kişi benim 0000-0001-8492-6262

Amor Kessab Bu kişi benim 0000-0001-6742-2759

Arezki Kheloufi Bu kişi benim 0000-0001-5584-1454

Yayımlanma Tarihi 6 Şubat 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 49 Sayı: 1

Kaynak Göster

APA 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, 49(1), 180-194. https://doi.org/10.15672/hujms.546340
AMA Cherfaoui S, Kessab A, Kheloufi A. Study of 2m-th order parabolic equation in non-symmetric conical domains. Hacettepe Journal of Mathematics and Statistics. Şubat 2020;49(1):180-194. doi:10.15672/hujms.546340
Chicago Cherfaoui, Saida, Amor Kessab, ve Arezki Kheloufi. “Study of 2m-Th Order Parabolic Equation in Non-Symmetric Conical Domains”. Hacettepe Journal of Mathematics and Statistics 49, sy. 1 (Şubat 2020): 180-94. https://doi.org/10.15672/hujms.546340.
EndNote Cherfaoui S, Kessab A, Kheloufi A (01 Şubat 2020) Study of 2m-th order parabolic equation in non-symmetric conical domains. Hacettepe Journal of Mathematics and Statistics 49 1 180–194.
IEEE S. Cherfaoui, A. Kessab, ve A. Kheloufi, “Study of 2m-th order parabolic equation in non-symmetric conical domains”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 1, ss. 180–194, 2020, doi: 10.15672/hujms.546340.
ISNAD Cherfaoui, Saida vd. “Study of 2m-Th Order Parabolic Equation in Non-Symmetric Conical Domains”. Hacettepe Journal of Mathematics and Statistics 49/1 (Şubat 2020), 180-194. https://doi.org/10.15672/hujms.546340.
JAMA Cherfaoui S, Kessab A, Kheloufi A. Study of 2m-th order parabolic equation in non-symmetric conical domains. Hacettepe Journal of Mathematics and Statistics. 2020;49:180–194.
MLA Cherfaoui, Saida vd. “Study of 2m-Th Order Parabolic Equation in Non-Symmetric Conical Domains”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 1, 2020, ss. 180-94, doi:10.15672/hujms.546340.
Vancouver Cherfaoui S, Kessab A, Kheloufi A. Study of 2m-th order parabolic equation in non-symmetric conical domains. Hacettepe Journal of Mathematics and Statistics. 2020;49(1):180-94.