Zobrazeno 1 - 7 of 7 pro vyhledávání: '"Łukasz Rzepnicki"'
1
Akademický článek
The basis property of eigenfunctions in the problem of a nonhomogeneous damped string
Autor: Łukasz Rzepnicki
Publikováno v: Opuscula Mathematica, Vol 37, Iss 1, Pp 141-165 (2017)
The equation which describes the small vibrations of a nonhomogeneous damped string can be rewritten as an abstract Cauchy problem for the densely defined closed operator \(i A\). We prove that the set of root vectors of the operator \(A\) forms a ba
Externí odkaz: https://doaj.org/article/8a4f6da32a8547ed8214d75381f0c9d6
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2
Akademický článek
Generating the exponentially stable C_{0}-semigroup in a nonhomogeneous string equation with damping at the end
Autor: Łukasz Rzepnicki
Publikováno v: Opuscula Mathematica, Vol 33, Iss 1, Pp 151-162 (2013)
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 \[\begin{cases} v_{tt}(x,t) - \frac{1}{\rho}v_{xx}(x,t) = 0, x \in [0,1], t \in [0, \in
Externí odkaz: https://doaj.org/article/f14d003486b54beea22fea2e5d4c02c2
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4
Asymptotic behavior of solutions of the Dirac system with an integrable potential
Autor: Łukasz Rzepnicki
We consider the Dirac system on the interval [0, 1] with a spectral parameter $$\mu \in {\mathbb {C}}$$ μ ∈ C and a complex-valued potential with entries from $$L_p[0,1]$$ L p [ 0 , 1 ] , where $$1\le p$$ 1 ≤ p . We study the asymptotic behavior
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::764bcde628e139f3aabd94b82a47e500
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7
Estimations of Solutions of the Sturm– Liouville Equation with Respect to a Spectral Parameter
Autor: Łukasz Rzepnicki
Publikováno v: Integral Equations and Operator Theory. 76:565-588
This paper is concerned with estimations of solutions of the Sturm–Liouville equation $$\big(p(x)y'(x)\big)'+\Big(\mu^2 -2i\mu d(x)-q(x)\Big)\rho(x)y(x)=0, \ \ x\in[0,1],$$ where $${\mu\in\mathbb{C}}$$ is a spectral parameter. We assume that the st
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c5293d583865f7fd933a1d8943d1656f
https://doi.org/10.1007/s00020-013-2071-3
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