Generating the exponentially stable C0-semigroup in a nonhomogeneous string equation with damping at the end

• Autorzy: Rzepnicki Ł.
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

nonhomogeneous string; one-dimensional wave equation; exponentially stable C0-semigroup; Hilbert space

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2013
• Tom: Vol. 33, no. 1
• Strony: 151--162
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Rzepnicki Ł.

• Nicolaus Copernicus University, Faculty of Mathematics and Computer Science, ul. Chopina 12/18, 87-100 Toruń, Poland,

Bibliografia

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