- Tytuł:
- On α-times integrated C-semigroups and the abstract Cauchy problem
- Autorzy:
-
Kuo, Chung-Cheng
Shaw, Sen-Yen - Powiązania:
- https://bibliotekanauki.pl/articles/1205940.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
generator
abstract Cauchy problem
α-times integrated C-semigroup - Opis:
- This paper is concerned with α-times integrated C-semigroups for α > 0 and the associated abstract Cauchy problem: $u'(t) = Au(t) + \frac{t^{α-1}}{Γ(α)}x$, t >0; u(0) = 0. We first investigate basic properties of an α-times integrated C-semigroup which may not be exponentially bounded. We then characterize the generator A of an exponentially bounded α-times integrated C-semigroup, either in terms of its Laplace transforms or in terms of existence of a unique solution of the above abstract Cauchy problem for every x in $(λ-A)^{-1}C(X)$.
- Źródło:
-
Studia Mathematica; 2000, 142, 3; 201-217
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł