Geodesic
Existence and analyticity of a parabolic evolution operator for nonautonomous linear equations in Banach spaces
Electronic journal of differential equations, Tome 2009 (2009)
We give conditions for the parabolic evolution operator to be analytic with respect to a coefficient operator. We also show that the solution of a homogeneous parabolic evolution equation is analytic with respect to the coefficient operator and to the initial data. We apply our results to example that can not be studied by the standard methods.
Classification : 35K90, 46T25, 47N20, 47L05
Keywords: linear equation, parabolic equation, nonautonomous 
@article{EJDE_2009__2009__a7,
     author = {Munhoz,  Antonio S. and Filho,  Antonio C.Souza},
     title = {Existence and analyticity of a parabolic evolution operator for nonautonomous linear equations in {Banach} spaces},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1173.35571},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a7/}
}
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Munhoz,  Antonio S.; Filho,  Antonio C.Souza. Existence and analyticity of a parabolic evolution operator for nonautonomous linear equations in Banach spaces. Electronic journal of differential equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a7/