Spectrum of the wave equation with Dirac damping on a non-compact star graph

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F23%3A00373042" target="_blank" >RIV/68407700:21340/23:00373042 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/proc/16412" target="_blank" >https://doi.org/10.1090/proc/16412</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/16412" target="_blank" >10.1090/proc/16412</a>

Result language
angličtina
Original language name
Spectrum of the wave equation with Dirac damping on a non-compact star graph
Original language description
We consider the wave equation on non-compact star graphs, subject to a distributional damping defined through a Robin-type vertex condition with complex coupling. It is shown that the non-self-adjoint generator of the evolution problem admits an abrupt change in its spectral properties for a special coupling related to the number of graph edges. As an application, we show that the evolution problem is highly unstable for the critical couplings. The relationship with the Dirac equation in non-relativistic quantum mechanics is also mentioned.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GX20-17749X" target="_blank" >GX20-17749X: New challenges for spectral theory: geometry, advanced materials and complex fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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