Geodesic
Fractional-power approach for solving complete elliptic abstract differential equations with variable-operator coefficients
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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].
Classification : 34G10, 34K10, 34K30, 35J25, 44A45, 47D03
Keywords: fractional powers of linear operators, analytic semigroup, strict solution, dunford's functional calculus 
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     author = {Boutaous, Fatiha and Labbas, Rabah and Sadallah, Boubaker-Khaled},
     title = {Fractional-power approach for solving complete elliptic abstract differential equations with variable-operator coefficients},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a24/}
}
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Boutaous, Fatiha; Labbas, Rabah; Sadallah, Boubaker-Khaled. Fractional-power approach for solving complete elliptic abstract differential equations with variable-operator coefficients. Electronic Journal of Differential Equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a24/