- Tytuł:
- Degenerate evolution problems and Beta-type operators
- Autorzy:
-
Attalienti, Antonio
Campiti, Michele - Powiązania:
- https://bibliotekanauki.pl/articles/1206074.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
approximation process
$C_0$-semigroups of contractions
Beta-type operators
differential operators - Opis:
- The present paper is concerned with the study of the differential operator Au(x):=α(x)u''(x)+β(x)u'(x) in the space C([0,1)] and of its adjoint Bv(x):=((αv)'(x)-β(x)v(x))' in the space $L^1(0,1)$, where α(x):=x(1-x)/2 (0≤x≤1). A careful analysis of their main properties is carried out in view of some generation results available in [6, 12, 20] and [25]. In addition, we introduce and study two different kinds of Beta-type operators as a generalization of similar operators defined in [18]. Among the corresponding approximation results, we show how they can be used in order to represent explicitly the solutions of the Cauchy problems associated with the operators A and Ã, where à is equal to B up to a suitable bounded additive perturbation.
- Źródło:
-
Studia Mathematica; 2000, 140, 2; 117-139
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł