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

KHELOUFI, Arezkı

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

Arezkı KHELOUFI (Işık Üniversitesi, Mühendislik Fakültesi, Matematik Bölümü, İstanbul, Türkiye)

TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics

1 0

Yıl: 2016 Cilt: 6 Sayı: 1 Sayfa Aralığı: 1 - 14 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

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

Öz:

In this paper, we look for sufficient conditions on the lateral surface ofthe domain and on the coefficients of the boundary conditions of a N-space dimensionallinear parabolic equation, in order to obtain existence, uniqueness and maximal regularityof the solution in a Hilbertian anisotropic Sobolev space when the right hand side of theequation is in a Lebesgue space. This work is an extension of solvability results obtainedfor a second order parabolic equation, set in a non-regular domain ofR3obtained in [1],to the case where the domain is cylindrical, not with respect to the time variable, butwith respect to N space variables, N > 1

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

Kheloufi,A., (2013), Existence and uniqueness results for parabolic equations with Robin type bound- ary conditions in a non-regular domain ofR3, Applied Mathematics and Computation, 220, pp. 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 ofR, 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 L1and W1p, Proc. Steklov Inst. Math. 89, pp. 5-17. p
Lions,J.L. and Magenes,E., (1968), Probl`emes aux Limites Non Homog `enes et Applications. 1,2, Dunod, Paris.

APA	KHELOUFI A (2016). ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OFRN +1. , 1 - 14.
Chicago	KHELOUFI Arezkı ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OFRN +1. (2016): 1 - 14.
MLA	KHELOUFI Arezkı ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OFRN +1. , 2016, ss.1 - 14.
AMA	KHELOUFI A ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OFRN +1. . 2016; 1 - 14.
Vancouver	KHELOUFI A ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OFRN +1. . 2016; 1 - 14.
IEEE	KHELOUFI A "ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OFRN +1." , ss.1 - 14, 2016.
ISNAD	KHELOUFI, Arezkı. "ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OFRN +1". (2016), 1-14.

APA	KHELOUFI A (2016). ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OFRN +1. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, 6(1), 1 - 14.
Chicago	KHELOUFI Arezkı ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OFRN +1. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics 6, no.1 (2016): 1 - 14.
MLA	KHELOUFI Arezkı ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OFRN +1. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, vol.6, no.1, 2016, ss.1 - 14.
AMA	KHELOUFI A ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OFRN +1. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics. 2016; 6(1): 1 - 14.
Vancouver	KHELOUFI A ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OFRN +1. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics. 2016; 6(1): 1 - 14.
IEEE	KHELOUFI A "ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OFRN +1." TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, 6, ss.1 - 14, 2016.
ISNAD	KHELOUFI, Arezkı. "ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OFRN +1". TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics 6/1 (2016), 1-14.