The improved decay rate for the heat semigroup with local magnetic field in the plane

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F13%3A00392916" target="_blank" >RIV/61389005:_____/13:00392916 - isvavai.cz</a>

Výsledek na webu

<a href="http://link.springer.com/content/pdf/10.1007%2Fs00526-012-0516-1.pdf" target="_blank" >http://link.springer.com/content/pdf/10.1007%2Fs00526-012-0516-1.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00526-012-0516-1" target="_blank" >10.1007/s00526-012-0516-1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The improved decay rate for the heat semigroup with local magnetic field in the plane

Popis výsledku v původním jazyce

We consider the heat equation in the presence of compactly supported magnetic field in the plane. We show that the magnetic field leads to an improvement of the decay rate of the heat semigroup by a polynomial factor with power proportional to the distance of the total magnetic flux to the discrete set of flux quanta. The proof employs Hardy-type inequalities due to Laptev and Weidl for the two-dimensional magnetic Schrodinger operator and the method of self-similar variables and weighted Sobolev spacesfor the heat equation. A careful analysis of the asymptotic behaviour of the heat equation in the similarity variables shows that the magnetic field asymptotically degenerates to an Aharonov-Bohm magnetic field with the same total magnetic flux, which leads asymptotically to the gain on the polynomial decay rate in the original physical variables. Since no assumptions about the symmetry of the magnetic field are made in the present work, it gives a normwise variant of the recent pointwi

Název v anglickém jazyce

The improved decay rate for the heat semigroup with local magnetic field in the plane

Popis výsledku anglicky

We consider the heat equation in the presence of compactly supported magnetic field in the plane. We show that the magnetic field leads to an improvement of the decay rate of the heat semigroup by a polynomial factor with power proportional to the distance of the total magnetic flux to the discrete set of flux quanta. The proof employs Hardy-type inequalities due to Laptev and Weidl for the two-dimensional magnetic Schrodinger operator and the method of self-similar variables and weighted Sobolev spacesfor the heat equation. A careful analysis of the asymptotic behaviour of the heat equation in the similarity variables shows that the magnetic field asymptotically degenerates to an Aharonov-Bohm magnetic field with the same total magnetic flux, which leads asymptotically to the gain on the polynomial decay rate in the original physical variables. Since no assumptions about the symmetry of the magnetic field are made in the present work, it gives a normwise variant of the recent pointwi

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BE - Teoretická fyzika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název periodika

Calculus of Variations and Partial Differential Equations

ISSN

0944-2669

e-ISSN

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Svazek periodika

47

Číslo periodika v rámci svazku

1-2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

207-226

Kód UT WoS článku

000317970100009

EID výsledku v databázi Scopus

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