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Parabolic equations with low regularity

Fontes, Magnus LU (1996)
Abstract (Swedish)
Popular Abstract in Swedish

Avhandlingen innehåller en ny metod att behandla ekvationer av den typ som styr t.ex. värmeledning och diffusion. Användning av ''halva derivator'' i tidsled möjliggör ett angreppssätt mycket likt den välkända Dirichlets princip inom elektrostatiken. Fördelen jämfört med existerande metoder är att den nya metoden ger en enkel och strömlinjeformad behandling av källtermer (exempelvis värmekällor) med mycket dåligt ''uppförande''. En väsentlig styrka hos metoden är dess användbarhet för vissa typer av icke-linjära ekvationer.
Abstract
In this work we study a variational method for treating parabolic equations that yields new results for non-linear equations with low regularity on source and boundary data. We treat mainly strongly parabolic quasilinear equations and systems in divergence form. The basic idea is to compose the parabolic operator with a weighted sum of the identity operator and the Hilbert transformation in the time direction, and in this way obtain a coercive operator. We work with functions having space derivatives in some Lp-space and half order time derivatives in L2. A key to our results is the celebrated theorem by Marcel Riesz concerning the boundedness of the Hilbert transformation on Lp-spaces when p is strictly greater than one.
Please use this url to cite or link to this publication:
author
opponent
  • Widman, Kjell, Institut Mittag-Leffler
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Matematik, Mathematics, Galerkin approximation., low regularity, variational method, Hilbert transformation, fractional calculus, parabolic equations, quasilinear
pages
56 pages
publisher
Department of Mathematics, Lund University
defense location
Department of Mathematics, room C
defense date
1996-09-20 10:15
external identifiers
  • other:ISRN LUTFD2/TFMA-96/1007-SE
ISSN
0347-8475
ISBN
91-628-2156-3
language
English
LU publication?
yes
id
8bcd4fc9-3668-4422-8579-760a82118415 (old id 17746)
date added to LUP
2007-05-24 09:02:03
date last changed
2016-09-19 08:44:56
@phdthesis{8bcd4fc9-3668-4422-8579-760a82118415,
  abstract     = {In this work we study a variational method for treating parabolic equations that yields new results for non-linear equations with low regularity on source and boundary data. We treat mainly strongly parabolic quasilinear equations and systems in divergence form. The basic idea is to compose the parabolic operator with a weighted sum of the identity operator and the Hilbert transformation in the time direction, and in this way obtain a coercive operator. We work with functions having space derivatives in some Lp-space and half order time derivatives in L2. A key to our results is the celebrated theorem by Marcel Riesz concerning the boundedness of the Hilbert transformation on Lp-spaces when p is strictly greater than one.},
  author       = {Fontes, Magnus},
  isbn         = {91-628-2156-3},
  issn         = {0347-8475},
  keyword      = {Matematik,Mathematics,Galerkin approximation.,low regularity,variational method,Hilbert transformation,fractional calculus,parabolic equations,quasilinear},
  language     = {eng},
  pages        = {56},
  publisher    = {Department of Mathematics, Lund University},
  school       = {Lund University},
  title        = {Parabolic equations with low regularity},
  year         = {1996},
}