Electron. J. Diff. Equ., Vol. 2012 (2012), No. 05, pp. 1-33.

Fractional-power approach for solving complete elliptic abstract differential equations with variable-operator coefficients

Fatiha Boutaous, Rabah Labbas, Boubaker-Khaled Sadallah

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
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
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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