The damped wave equation with unbounded damping

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

The damped wave equation with unbounded damping

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

The damped wave equation with unbounded damping

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

—

Svazek periodika

264

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

32

Strana od-do

7023-7054

Kód UT WoS článku

000430280100001

EID výsledku v databázi Scopus

2-s2.0-85042165079