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

• Autorzy: Anastasie Gudovich , Mikhail Kamenski , Paolo Nistri
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

singular perturbations; differential inclusions; analytic semigroups; multivalued compact operators; Lipschitz selections

Kategorie tematyczne

• 47H04: Set-valued operators
• 34D15: Singular perturbations
• 34G25: Evolution inclusions
• 54C65: Selections

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2001
• Tom: 21
• Numer: 2
• Strony: 207-234

Daty

wydano

2001

otrzymano

2001-08-18

Twórcy

autor

Anastasie Gudovich

• Department of Applied Mathematics and Mechanics, Voronezh State University, Voronezh, Russia

autor

Mikhail Kamenski

• Faculty of Mathematics, Voronezh State University, Universitetskaya pl., 1, 394693, Voronezh, Russia

autor

Paolo Nistri

• Department of Information Engineering, University of Siena, 53100 Siena, Italy

Bibliografia

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• [6] M. Kamenskii and P. Nistri, Periodic solutions of a singularly perturbed systems of differential inclusions in Banach spaces, in: Set-Valued Mappings with Applications in Nonlinear Analysis, Series in Mathematical Analysis and Applications 4, Gordon and Breach Science Publishers, London 2001, 213-226.
• [7] M. Krasnoselskii, P. Zabreiko, E. Pustyl'nik, and P. Sobolevski, Integral Operators in Spaces of Summable Functions, Noordhoff International Publishing, Leyden 1976.
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Identyfikatory

DOI

10.7151/dmgt.1025