Boubaker-Khaled Sadallah

On a parabolic equation in a triangular domain

We prove the optimal regularity, in Sobolev spaces, of the solution of a parabolic equation set in a triangular domain T. The right-hand term of the equation is taken in Lebesgue space L^p(T). The method of operators sums in the non-commutative case is referred to.

Sur une équation parabolique dans un domaine non cylindrique

We give some results about the optimal regularity of a solution to a parabolic equation, set in non cylindrical domains U=⋃t∈]0,1[{t}× It with It={x:0 1/2 is considered and the optimal regularity is obtained when the second member is regular. We use Labbas and Terrenis results [7]. This study is generalized when ϕϕ′ is Holderian. The second model corresponds to the limit case ϕ(t)=t and the maximal regularity is obtained for second members taken only in Lp(U), 1<p<∞. Here, we use Dore–Vennis results [3]. To cite this article: R. Labbas et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 1017–1022.

On the regularity of the heat equation solution in non-cylindrical domains: Two approaches

Abstract In this work, we investigate the behavior of the solution of the Cauchy–Dirichlet problem for a parabolic equation set in a three-dimensional domain with edges. We also give new regularity results for the weak solution of this equation in terms of the regularity of the initial data.

On a degenerate parabolic problem in Hölder spaces

In this paper, we study some degenerate parabolic equation with Cauchy-Dirichlet boundary conditions. This problem is considered in little Holder spaces. The optimal regularity of the solution v is obtained and is specified in terms of those of the second member when some conditions upon the Holder exponent with respect to the degeneracy are satisfied. The proofs mainly use the sum theory of linear operators with or without density of domains and the results of smoothness obtained in the study of some abstract linear differential equations of elliptic type.

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

This work is concerned with the problem @tu c(t)@ 2u = f u|@D\0T = 0 posed in the domain D = {(t, x) 2 R 2 | 0< t < T, ’1(t) < x < ’2(t)}, which is not necessary rectangular, and with 0T = {(T, x) |’1(T) < x < ’2(T)}.

RESOLUTION IN H ¨ OLDER SPACES OF AN ELLIPTIC PROBLEM IN AN UNBOUNDED DOMAIN

In this paper we give new results concerning the maximal regularity of the strict solution of an abstract second-order differential equation, with non-homogeneous boundary conditions of Dirichlet type, and set in an unbounded interval. The right-hand term of the equation is a Holder continuous function.