Joel Blot, Philippe Cieutat, Gaston M. N'Guerekata
Abstract:
We consider the semilinear evolution equations
and
where
is a unbounded linear operator on a Banach space X and f
is a nonlinear operator. We study the dependence of solutions
x with respect to the function
in three cases: the continuous
almost periodic functions, the differentiable almost periodic
functions, and the almost automorphic functions. We give results
on the continuous dependence and on the differentiable dependence.
Submitted May 25, 2010. Published July 21, 2010.
Math Subject Classifications: 47J35, 43A60, 47D06.
Key Words: Semilinear evolution equation; almost periodic function;
almost automorphic function; dependence results.
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Joël Blot Laboratoire SAMM EA 4543, Université Paris 1 Panthéon-Sorbonne centre P.M.F., 90 rue de Tolbiac, 75634 Paris cedex 13, France email: blot@univ-paris1.fr | |
Philippe Cieutat Laboratoire de Mathématiques de Versailles, UMR-CNRS 8100 Université Versailles-Saint-Quentin-en-Yvelines 45 avenue des États-Unis, 78035 Versailles cedex, France email: Philippe.Cieutat@math.uvsq.fr | |
Gaston M. N'Guérékata Department of Mathematics Morgan State University 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA email: gnguerek@jewel.morgan.edu |
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