Temat: exponentially stable - Katalog OPAC zbiorów

Skocz do pozycji: 1.

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

Skocz do pozycji: 2.

Tytuł:: On \(C^{(n)}\)-Almost Periodic Solutions to Some Nonautonomous Differential Equations in Banach Spaces
Autorzy:: Baillon, Jean-Bernard
Blot, Joël
N'Guérékata, Gaston M.
Pennequin, Denis
Powiązania:: https://bibliotekanauki.pl/articles/746570.pdf
Data publikacji:: 2006
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: \(C^{(n)}\)-almost periodic function
family of bounded operators
exponentially stable
Acquistapace-Terreni conditions
uniform spectrum of bounded functions
Opis:: In this paper we prove the existence and uniqueness of \(C^{(n)}\)-almost periodic solutions to the nonautonomous ordinary differential equation \(x'(t) = A(t)x(t) + f(t)\), \(t\in\mathbb{R}\), where \(A(t)\) generates an exponentially stable family of operators \((U (t, s))\) \(t\geq s\) and \(f\) is a \(C^{(n)}\)-almost periodic function with values in a Banach space \(X\). We also study a Volterra-like equation with a \(C^{(n)}\)-almost periodic solution.
Źródło:: Commentationes Mathematicae; 2006, 46, 2
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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