Geodesic
A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 21 (2001) no. 2, pp. 207-234.

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We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for ε ≥ 0, where ε is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset Z_L(ε) of the solution set of the singularly perturbed system. This subset is the set of the Hölder continuous solutions defined in [0,d], d > 0 with prescribed exponent and constant L. We show that Z_L(ε) is uppersemicontinuous at ε = 0 in the C[0,d]×C[δ,d] topology for any δ ∈ (0,d].
Keywords: singular perturbations, differential inclusions, analytic semigroups, multivalued compact operators, Lipschitz selections 
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Gudovich, Anastasie; Kamenski, Mikhail; Nistri, Paolo. A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 21 (2001) no. 2, pp. 207-234. http://geodesic.mathdoc.fr/item/DMDICO_2001_21_2_a3/

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