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Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic field

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Hamiltonian VWS_2016.10.07_2.pdfAccepted version181.37 kBAdobe PDFView/Open
10.1007%2Fs11005-016-0919-6.pdfPublished version584.4 kBAdobe PDFView/Open
Title: Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic field
Authors: Ruzhansky, M
Tokmagambetov, N
Item Type: Journal Article
Abstract: In this paper we study the Cauchy problem for the Landau Hamiltonian wave equation, with time dependent irregular (distributional) electromagnetic field and similarly irregular velocity. For such equations, we describe the notion of a ‘very weak solution’ adapted to the type of solutions that exist for regular coef- ficients. The construction is based on considering Friedrichs–type mollifier of the coefficients and corresponding classical solutions, and their quantitative behaviour in the regularising parameter. We show that even for distributional coefficients, the Cauchy problem does have a very weak solution, and that this notion leads to classical or distributional type solutions under conditions when such solutions also exist.
Issue Date: 21-Nov-2016
Date of Acceptance: 7-Oct-2016
URI: http://hdl.handle.net/10044/1/41310
DOI: https://dx.doi.org/10.1007/s11005-016-0919-6
ISSN: 1573-0530
Publisher: Springer Verlag (Germany)
Start Page: 591
End Page: 618
Journal / Book Title: Letters in Mathematical Physics
Volume: 107
Copyright Statement: © The Author(s) 2016. This article is published with open access at Springerlink.com
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Funder's Grant Number: EP/K039407/1
RPG-2014-002
Keywords: Science & Technology
Physical Sciences
Physics, Mathematical
Physics
Wave equation
Well-posedness
Electromagnetic field
Cauchy problem
Landau Hamiltonian
MAGNETIC SCHRODINGER-OPERATORS
SPECTRAL PROPERTIES
CAUCHY-PROBLEM
TRACE FORMULA
COEFFICIENTS
EIGENFUNCTIONS
PERTURBATIONS
ASYMPTOTICS
REGULARITY
math.AP
math.FA
math.SP
35D99, 35L81, 35Q99, 42C10, 58J45
01 Mathematical Sciences
02 Physical Sciences
Mathematical Physics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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