Polynomial energy decay of a wave–Schrödinger transmission system

We study in this paper a wave–Schrödinger transmission system for its stability. By analyzing carefully Green’s functions for the infinitesimal generator of the semigroup associated with the system under consideration, we obtain a useful resolvent estimate on this generator which can be applied to d...

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Bibliographic Details
Published inBoundary value problems Vol. 2018; no. 1; pp. 1 - 14
Main Author Wang, Chengqiang
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 24.04.2018
Hindawi Limited
SpringerOpen
Subjects
Analysis
Approximations and Expansions
Decay
Difference and Functional Equations
Energy transmission
Green’s functions
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Polynomial energy decay
Resolvent estimate
Stability analysis
Wave–Schrödinger transmission system
Wave–Schrödinger transmission system
Polynomial energy decay
35P05
35B35
Green’s functions
35C20
Resolvent estimate
35B30
35Q41
35L10
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Summary:We study in this paper a wave–Schrödinger transmission system for its stability. By analyzing carefully Green’s functions for the infinitesimal generator of the semigroup associated with the system under consideration, we obtain a useful resolvent estimate on this generator which can be applied to derive the decaying property. Our study is inspired by L. Lu & J.-M. Wang [Appl. Math. Lett., 54:7–14, 2016 ] whose energy decay result is improved upon in our paper. Our method, different from the one used in the previous reference, can be adapted to study stability problems for other 1-D transmission systems.
ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-018-0978-y