The damped wave equation with unbounded damping
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F18%3A00489299" target="_blank" >RIV/61389005:_____/18:00489299 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jde.2018.02.010" target="_blank" >http://dx.doi.org/10.1016/j.jde.2018.02.010</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2018.02.010" target="_blank" >10.1016/j.jde.2018.02.010</a>
Alternative languages
Result language
angličtina
Original language name
The damped wave equation with unbounded damping
Original language description
We analyze new phenomena arising in linear damped wave equations on unbounded domains when the damping is allowed to become unbounded at infinity. We prove the generation of a contraction semigroup, study the relation between the spectra of the semigroup generator and the associated quadratic operator function, the convergence of non-real eigenvalues in the asymptotic regime of diverging damping on a subdomain, and we investigate the appearance of essential spectrum on the negative real axis. We further show that the presence of the latter prevents exponential estimates for the semigroup and turns out to be a robust effect that cannot be easily canceled by adding a positive potential. These analytic results are illustrated by examples.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Differential Equations
ISSN
0022-0396
e-ISSN
—
Volume of the periodical
264
Issue of the periodical within the volume
12
Country of publishing house
US - UNITED STATES
Number of pages
32
Pages from-to
7023-7054
UT code for WoS article
000430280100001
EID of the result in the Scopus database
2-s2.0-85042165079