Fatiha Boutaous, Rabah Labbas, Boubaker-Khaled Sadallah
Abstract:
This work is devoted to the study of a complete abstract
second-order differential equation of elliptic type with
variable operators as coefficients.
A similar equation was studied by Favini et al [6] using
Green's kernels and Dunford functional calculus. Our approach
is based on the semigroup theory, the fractional powers
of linear operators, and the Dunford's functional calculus.
We will prove the main result on the existence and uniqueness
of a strict solutions using combining assumptions from
Yagi [16], Da Prato-Grisvard [3], and Acquistapace-Terreni [1].
Submitted June 14, 2011. Published January 9, 2012.
Math Subject Classifications: 34G10, 34K10, 34K30,35J25, 44A45, 47D03.
Key Words: Fractional powers of linear operators; analytic semigroup;
strict solution; Dunford's functional calculus.
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Fatiha Boutaous Département de Mathématiques, Faculté des Sciences Université Saád Dahlab, B.P. 270, Blida, Algérie email: boutaous.fatiha2009@hotmail.com |
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Rabah Labbas Laboratoire de Mathématiques Appliquées Université du Havre, UFR ST, B.P. 540 76058 Le Havre Cedex, France email: rabah.labbas@univ-lehavre.fr |
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Boubaker-Khaled Sadallah Laboratoire des EDP et Histoire des Mathématiques Ecole Normale Supérieure 16050 Kouba, Alger, Algérie email: sadallah@ens-kouba.dz |
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