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REGULARITY OF A PARABOLIC EQUATION SOLUTION IN A NONSMOOTH AND UNBOUNDED DOMAIN

Part of: Parabolic equations and systems

Published online by Cambridge University Press:  01 April 2008

BOUBAKER-KHALED SADALLAH
BOUBAKER-KHALED SADALLAH*
Affiliation:
Laboratoire Equations aux Dérivées Partialles et Histoire des Mathématiques, Department of Mathematics, École Normale Supérieure, 16050-Kouba, Algiers, Algeria (email: sadallah@ens-kouba.dz)
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Abstract

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This work is concerned with the problem posed in the domain which is not necessary rectangular, and with Our goal is to find some conditions on the coefficient c and the functions ( φi) i=1,2 such that the solution of this problem belongs to the Sobolev space

Keywords

parabolicheat equationnonsmooth domainsectorial

MSC classification

Secondary: 35K05: Heat equation 35K20: Initial-boundary value problems for second-order parabolic equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 2 , April 2008 , pp. 265 - 276
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Alkhutov, Yu. A. and Mamedov, I. T., ‘The first boundary value problem for nondivergence second-order parabolic equations with discontinuous coefficients’, Russian Acad. Sc. Sbornik Math. 59(2) (1988), 471–495.Google Scholar
[2]Azzam, A., ‘On behavior of solution of elliptic and parabolic equations at a crack’, Hokkaido Math. J. 19(2) (1990), 339–344.Google Scholar
[3]Baderko, E. A., ‘Étude du problème de Dirichlet pour une équation 2p-parabolique dans un domaine non rectangulaire’, C. R. Math. Acad. Sci. Paris 287 (1978), 221–224.Google Scholar
[4]Partial Differential Equations and Functional Analysis in Memory of Pierre Grisvard (ed. J. Cea et al.) (Birkhäuser, Basel, 1996).Google Scholar
[5]Dauge, M., Elliptic Boundary Value Problems on Corner Domains (Springer, Berlin, 1988).Google Scholar
[6]Grisvard, P., Elliptic Problems in Non-smooth Domains, Monographs and Studies in Mathematics, 24 (Pitman, Boston, MA, 1985).Google Scholar
[7]Grisvard, P., Singularities in Boundary Value Problems, RMA, 22 (Masson, Paris, 1992).Google Scholar
[8]Grisvard, P., Problèmes aux limites dans des domaines avec points de rebroussement, in: Partial Differential Equations and Functional Analysis in Memory of P. Grisvard (Birkhäuser, Basel, 1996), pp. 1–17.Google Scholar
[9]Ibuki, K., ‘On the regularity of a mixed problem for hyperbolic equation of second order in a domain with corners’, J. Math. Kyoto Univ. 16(1) (1976), 167–183.Google Scholar
[10]Kondratiev, V. A., ‘Boundary-value problems for elliptic equations in domains with conical or angular points’, Trans. Moscow Math. Soc. 16 (1967), 227–313.Google Scholar
[11]Labbas, R. and Moussaoui, M., ‘On the resolution of the heat equation with discontinuous coefficients’, Semigroup Forum 60 (2000), 187–201.Google Scholar
[12]Labbas, R. and Sadallah, B.-K., ‘Smoothness of the solution of a fourth order parabolic equation in a polygonal domain’, Int. J. Appl. Math. 1(1) (1999), 75–90.Google Scholar
[13]Labbas, R., Medeghri, A. and Sadallah, B.-K., ‘On a parabolic equation in a triangular domain’, Appl. Math. Comput. 130(2–3) (2002), 511–523.Google Scholar
[14]Labbas, R., Medeghri, A. and Sadallah, B.-K., ‘Sur une équation parabolique dans un domaine non cylindrique’, C. R. Math. Acad. Sci. Paris 335(12) (2002), 1017–1022.Google Scholar
[15]Lions, J.-L. and Magenes, E., Problèmes aux limites non homogènes et applications, Vol. 2 (Dunod, Paris, 1968).Google Scholar
[16]Maz’ja, V. G. and Plamenevskii, B. A., ‘Weighed spaces with nonhomogeneous norms and boundary value problems in domains with conical points’, Amer. Math. Soc. Transl. 2(123) (1984), 89–107.Google Scholar
[17]Moussaoui, M. and Sadallah, B.-K., ‘Régularité des coefficients de propagation de singularités pour l’Equation de la Chaleur dans un Ouvert Plan polygonal’, C. R. Math. Acad. Sci. Paris 293(5) (1981), 297–300.Google Scholar
[18]Nicaise, S., ‘Regularity of the solutions of elliptic systems in polyhedral domains’, Bull. Belg. Math. Soc. Simon Stevin 4 (1997), 411–429.Google Scholar
[19]Sadallah, B.-K., ‘Étude d’un problème 2m-parabolique dans des domaines plans non rectangulaires’, Boll. U. M. I. B. (6) 2(1) (1983), 51–112.Google Scholar
[20]Taniguchi, M., ‘Initial boundary value problem for the wave equation in a domain with a corner’, Tokyo J. Math. 16(1) (1993), 61–98.Google Scholar