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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BE - Theoretical physics

OECD FORD branch

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Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2013

Confidentiality

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

Name of the periodical

Calculus of Variations and Partial Differential Equations

ISSN

0944-2669

e-ISSN

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Volume of the periodical

47

Issue of the periodical within the volume

1-2

Country of publishing house

US - UNITED STATES

Number of pages

20

Pages from-to

207-226

UT code for WoS article

000317970100009

EID of the result in the Scopus database

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