- Tytuł:
- Generating the exponentially stable C0-semigroup in a nonhomogeneous string equation with damping at the end
- Autorzy:
- Rzepnicki, Ł.
- Powiązania:
- https://bibliotekanauki.pl/articles/254708.pdf
- Data publikacji:
- 2013
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
nonhomogeneous string
one-dimensional wave equation
exponentially stable C0-semigroup
Hilbert space - Opis:
- Small vibrations of a nonhomogeneous string of length one with left end fixed and right one moving with damping are described by the one-dimensional wave equation [formula] where ρ is the density of the string and h is a complex parameter. This equation can be rewritten in an operator form as an abstract Cauchy problem for the closed, densely defined operator B acting on a certain energy space H. It is proven that the operator B generates the exponentially stable C0-semigroup of contractions in the space H under assumptions that Re h > 0 and the density function is of bounded variation satisfying 0 < m ≤ ρ(x) for a.e. x ∈ [0; 1].
- Źródło:
-
Opuscula Mathematica; 2013, 33, 1; 151-162
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł