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A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces

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Gudovich A., Kamenski M., Nistri P.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2001

tom 21

nr 2

207-234

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].

Ograniczanie wyników

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Gudovich A.

1 Kamenski M.

1 Nistri P.

1 2001

Wyniki wyszukiwania

A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces