- Tytuł:
- A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces
- Autorzy:
-
Gudovich, Anastasie
Kamenski, Mikhail
Nistri, Paolo - Powiązania:
- https://bibliotekanauki.pl/articles/729318.pdf
- Data publikacji:
- 2001
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
singular perturbations
differential inclusions
analytic semigroups
multivalued compact operators
Lipschitz selections - Opis:
- 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].
- Źródło:
-
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 2; 207-234
1509-9407 - Pojawia się w:
- Discussiones Mathematicae, Differential Inclusions, Control and Optimization
- Dostawca treści:
- Biblioteka Nauki
Artykuł