BibTex RIS Kaynak Göster
Yıl 2016, Cilt: 6 Sayı: 1, 1 - 14, 01.06.2016

Öz

Kaynakça

  • Kheloufi,A., (2013), Existence and uniqueness results for parabolic equations with Robin type bound- ary conditions in a non-regular domain of R3, Applied Mathematics and Computation, 220, pp. 756-769.
  • Sadallah,B.K., (1983), Etude d’un probl`eme 2m-parabolique dans des domaines plan non rectangu- laires. Boll. Un. Mat. Ital., 2-B (5), pp. 51-112.
  • Alkhutov,Yu.A., (2007), Lp-Estimates of solutions of the Dirichlet problem for the heat equation in a ball. Journ. Math. Sc., 142 (3), pp. 2021-2032.
  • Kheloufi,A., Labbas,R. and Sadallah,B.K., (2010), On the resolution of a parabolic equation in a non-regular domain of R3, Differential Equations and Applications, 2 (2),pp. 251-263.
  • Labbas,R., Medeghri,A. and Sadallah,B.K., (2002), Sur une ´equation parabolique dans un domaine non cylindrique. C.R.A.S, Paris, 335, pp. 1017-1022.
  • Labbas,R., Medeghri,A. and Sadallah,B.K., (2002), On a parabolic equation in a triangular domain. Applied Mathematics and Computation 130, pp. 511-523.
  • Labbas,R., Medeghri,A. and Sadallah,B.K., (2005), An Lpapproach for the study of degenerate parabolic equation. E. J. D.E., 2005 (36), pp. 1-20.
  • Sadallah,B.K., (2008), Regularity of a parabolic equation solution in a non-smooth and unbounded domain. J. Aust. Math. Soc., 84 (2), pp. 265-276.
  • Sadallah,B.K., (2008), A remark on a parabolic problem in a sectorial domain. Applied Mathematics E-Notes, 8, pp. 263-270.
  • Nazarov,A.I., (2001), Lp−estimates for a solution to the Dirichlet problem and to the Neumann problem for the heat equation in a wedge with edge of arbitrary codimension. J. Of Math.Sci., 106, (3), pp. 2989-3014.
  • Savar´e,G., (1997), Parabolic problems with mixed variable lateral conditions: an abstract approach. J. Math. Pures et Appl. 76, pp. 321-351.
  • Kheloufi,A. and Sadallah,B.K., (2010), Parabolic equations with Robin type boundary conditions in a non-rectangular domain. E.J.D.E., (25), pp. 1-14.
  • Ladyzhenskaya,O. A., Solonnikov,V.A. and Ural’tseva,N. N., (1968), Linear and Quasi-Linear Equa- tions of Parabolic Type, A.M.S., providence, Rhode Island.
  • Besov,V., (1967), The continuation of function in Lpand W1p, Proc. Steklov Inst. Math. 89, pp. 5-17. [15] Lions,J.L. and Magenes,E., (1968), Probl`emes aux Limites Non Homog `enes et Applications. 1,2, Dunod, Paris.
  • Arezki Kheloufi for the photography and short autobiography, see TWMS J. App. Eng. Math., V.5, N.1.

ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OF RN+1

Yıl 2016, Cilt: 6 Sayı: 1, 1 - 14, 01.06.2016

Öz

In this paper, we look for sucient conditions on the lateral surface of the domain and on the coecients of the boundary conditions of a Nspace dimensional linear parabolic equation, in order to obtain existence, uniqueness and maximal regularity of the solution in a Hilbertian anisotropic Sobolev space when the right hand side of the equation is in a Lebesgue space. This work is an extension of solvability results obtained for a second order parabolic equation, set in a non-regular domain of R3 obtained in [1], to the case where the domain is cylindrical, not with respect to the time variable, but with respect to N space variables, N > 1

Kaynakça

  • Kheloufi,A., (2013), Existence and uniqueness results for parabolic equations with Robin type bound- ary conditions in a non-regular domain of R3, Applied Mathematics and Computation, 220, pp. 756-769.
  • Sadallah,B.K., (1983), Etude d’un probl`eme 2m-parabolique dans des domaines plan non rectangu- laires. Boll. Un. Mat. Ital., 2-B (5), pp. 51-112.
  • Alkhutov,Yu.A., (2007), Lp-Estimates of solutions of the Dirichlet problem for the heat equation in a ball. Journ. Math. Sc., 142 (3), pp. 2021-2032.
  • Kheloufi,A., Labbas,R. and Sadallah,B.K., (2010), On the resolution of a parabolic equation in a non-regular domain of R3, Differential Equations and Applications, 2 (2),pp. 251-263.
  • Labbas,R., Medeghri,A. and Sadallah,B.K., (2002), Sur une ´equation parabolique dans un domaine non cylindrique. C.R.A.S, Paris, 335, pp. 1017-1022.
  • Labbas,R., Medeghri,A. and Sadallah,B.K., (2002), On a parabolic equation in a triangular domain. Applied Mathematics and Computation 130, pp. 511-523.
  • Labbas,R., Medeghri,A. and Sadallah,B.K., (2005), An Lpapproach for the study of degenerate parabolic equation. E. J. D.E., 2005 (36), pp. 1-20.
  • Sadallah,B.K., (2008), Regularity of a parabolic equation solution in a non-smooth and unbounded domain. J. Aust. Math. Soc., 84 (2), pp. 265-276.
  • Sadallah,B.K., (2008), A remark on a parabolic problem in a sectorial domain. Applied Mathematics E-Notes, 8, pp. 263-270.
  • Nazarov,A.I., (2001), Lp−estimates for a solution to the Dirichlet problem and to the Neumann problem for the heat equation in a wedge with edge of arbitrary codimension. J. Of Math.Sci., 106, (3), pp. 2989-3014.
  • Savar´e,G., (1997), Parabolic problems with mixed variable lateral conditions: an abstract approach. J. Math. Pures et Appl. 76, pp. 321-351.
  • Kheloufi,A. and Sadallah,B.K., (2010), Parabolic equations with Robin type boundary conditions in a non-rectangular domain. E.J.D.E., (25), pp. 1-14.
  • Ladyzhenskaya,O. A., Solonnikov,V.A. and Ural’tseva,N. N., (1968), Linear and Quasi-Linear Equa- tions of Parabolic Type, A.M.S., providence, Rhode Island.
  • Besov,V., (1967), The continuation of function in Lpand W1p, Proc. Steklov Inst. Math. 89, pp. 5-17. [15] Lions,J.L. and Magenes,E., (1968), Probl`emes aux Limites Non Homog `enes et Applications. 1,2, Dunod, Paris.
  • Arezki Kheloufi for the photography and short autobiography, see TWMS J. App. Eng. Math., V.5, N.1.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

A. Kheloufi Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 6 Sayı: 1

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