On $2m$-th order parabolic equations with mixed boundary conditions in~non-rectangular domains
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 73-91.

Voir la notice de l'article provenant de la source Math-Net.Ru

This article is devoted to the analysis of a one-space dimensional high-order parabolic equation, subject to mixed boundary conditions. The problem is set in a (possibly non-regular) non-rectangular domain and the right hand side term of the equation is taken in a Lebesgue space.
Keywords: high-order parabolic equations, mixed conditions
Mots-clés : anisotropic Sobolev spaces, non-rectangular domains.
@article{SEMR_2017_14_a84,
     author = {S. Cherfaoui and A. Kessab and A. Kheloufi},
     title = {On $2m$-th order parabolic equations with mixed boundary conditions in~non-rectangular domains},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {73--91},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a84/}
}
TY  - JOUR
AU  - S. Cherfaoui
AU  - A. Kessab
AU  - A. Kheloufi
TI  - On $2m$-th order parabolic equations with mixed boundary conditions in~non-rectangular domains
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2017
SP  - 73
EP  - 91
VL  - 14
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2017_14_a84/
LA  - en
ID  - SEMR_2017_14_a84
ER  - 
%0 Journal Article
%A S. Cherfaoui
%A A. Kessab
%A A. Kheloufi
%T On $2m$-th order parabolic equations with mixed boundary conditions in~non-rectangular domains
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2017
%P 73-91
%V 14
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2017_14_a84/
%G en
%F SEMR_2017_14_a84
S. Cherfaoui; A. Kessab; A. Kheloufi. On $2m$-th order parabolic equations with mixed boundary conditions in~non-rectangular domains. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 73-91. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a84/

[1] 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, M., 1992

[2] O. V. Besov, “Continuation of functions from $L\sb{p}{}\sp{l}$ and $W\sb{p}{}\sp{l}$”, Trudy Mat. Inst. Steklov, 89, 1967, 5–17 | MR | Zbl

[3] A. Cabada, R. Precup, L. Saavedra, S. Tersian, “Multiple positive solutions to a fourth order boundary value problem”, Electronic Journal of Differential Equations, 2016 (2016), 1–18 | MR | Zbl

[4] J. Dugundji, “Cantilever boundary condition, deflections, and stresses of sandwich beams”, AIAA Journal, 40:5 (2002), 987–995 | DOI

[5] M. F. Cherepova, “Regularity of solutions of boundary value problems for a second-order parabolic equation in weighted Hölder spaces”, Differ. Uravn., 49:1 (2013), 79–87 | DOI | MR | Zbl

[6] V. A. Galaktionov, “On regularity of a boundary point for higher-order parabolic equations: towards Petrovskii-type criterion by blow-up approach”, Nonlinear Differential Equations Appl., 16:5 (2009), 597–655 | DOI | MR | Zbl

[7] A. Grimaldi Piro, F. Ragnedda, “Parabolic operators of higher order in domains with a “non regular” boundary”, Rend. Sem. Fac.Sci. Univ. Cagliari, 54 (1984), 45–62 | MR | Zbl

[8] A. Kheloufi, “On a fourth order parabolic equation in a nonregular domain of $ \mathbb{R} ^{3}$”, Mediterr. J. Math., 12 (2015), 803–820 | DOI | MR | Zbl

[9] A. Kheloufi, B. K. Sadallah, “Study of a parabolic equation with mixed Dirichlet–Neumann type boundary conditions in unbounded noncylindrical domains”, Journal of Advanced Research in Applied Mathematics, 7:4 (2015), 62–77 | MR

[10] A. Kheloufi, “On a Fourth Order Parabolic Equation with Mixed Type Boundary Conditions in a Nonrectangular Domain”, Moroccan J. Pure and Appl. Anal., 1:2 (2015), 76–90

[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 (2016), 227–237 | DOI | MR | Zbl

[12] A. Kheloufi, B. K. Sadallah, “Resolution of a high-order parabolic equation in conical time-dependent domains of $ \mathbb{R} ^{3}$”, Arab. J. Math. Sci., 22 (2016), 165–181 | DOI | MR | Zbl

[13] V. A. Kondrat'ev, “Boundary problems for parabolic equations in closed regions”, Trans. Moscow Math. Soc., 15, Am. Math. Soc., Providence, R. I., 1966, 450–504 | MR | Zbl

[14] R. Labbas, B. K. Sadallah, “Smoothness of the solution of a fourth order parabolic equation in a polygonal domain”, Int. J. Appl. Math., 1 (1999), 75–90 | MR | Zbl

[15] J. L. Lions, E. Magenes, Problèmes aux limites non homogènes et applications, v. 1, 2, Dunod, Paris, 1968 | MR | Zbl

[16] V. P. Mikhailov, “The Dirichlet problem for a parabolic equation I”, Mat. Sb. (N.S.), 61(103) (1963), 40–64 | MR

[17] V. P. Mikhailov, “The Dirichlet problem for a parabolic equation II”, Mat. Sb. (N.S.), 62(104) (1963), 140–159 | MR

[18] B. K. Sadallah, “Etude d'un problème $2m$-parabolique dans des domaines plan non rectangulaires”, Boll. Un. Mat. Ital., 2-B:5 (1983), 51–112 | MR | Zbl

[19] B. K. Sadallah, “Singularities of the solution of a $2m$-parabolic problem in a polygonal domain”, Arab. J. Math. Sci., 4:2 (1998), 31–41 | MR | Zbl

[20] G. Savaré, “Parabolic problems with mixed variable lateral conditions: an abstract approach”, J. Math. Pures Appl., 76:9 (1997), 321–351 | DOI | MR | Zbl

[21] G. Shi, G. Z. Voyiadjis, “A sixth-order theory of shear deformable beams with variational consistent boundary conditions”, J. Appl. Mech., 78:2 (2010), 1–11