Energy method for multi-dimensional balance laws with non-local dissipation

Handle URI:
http://hdl.handle.net/10754/598168
Title:
Energy method for multi-dimensional balance laws with non-local dissipation
Authors:
Duan, Renjun; Fellner, Klemens; Zhu, Changjiang
Abstract:
In this paper, we are concerned with a class of multi-dimensional balance laws with a non-local dissipative source which arise as simplified models for the hydrodynamics of radiating gases. At first we introduce the energy method in the setting of smooth perturbations and study the stability of constants states. Precisely, we use Fourier space analysis to quantify the energy dissipation rate and recover the optimal time-decay estimates for perturbed solutions via an interpolation inequality in Fourier space. As application, the developed energy method is used to prove stability of smooth planar waves in all dimensions n2, and also to show existence and stability of time-periodic solutions in the presence of the time-periodic source. Optimal rates of convergence of solutions towards the planar waves or time-periodic states are also shown provided initially L1-perturbations. © 2009 Elsevier Masson SAS.
Citation:
Duan R, Fellner K, Zhu C (2010) Energy method for multi-dimensional balance laws with non-local dissipation. Journal de Mathématiques Pures et Appliquées 93: 572–598. Available: http://dx.doi.org/10.1016/j.matpur.2009.10.007.
Publisher:
Elsevier BV
Journal:
Journal de Mathématiques Pures et Appliquées
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
Jun-2010
DOI:
10.1016/j.matpur.2009.10.007
Type:
Article
ISSN:
0021-7824
Sponsors:
R.-J. Duan would like to thank Prof. Peter Markowich and Dr. Massimo Fornasier for their support during the postdoctoral studies of the year 2008-2009 in RICAM. K. Fellner's work has been supported by the KAUST Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST). The research of C.-J. Zhu was supported by the National Natural Science Foundation of China #10625105 and The Key Laboratory of Mathematical Physics of Hubei Province.
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Full metadata record

DC FieldValue Language
dc.contributor.authorDuan, Renjunen
dc.contributor.authorFellner, Klemensen
dc.contributor.authorZhu, Changjiangen
dc.date.accessioned2016-02-25T13:13:59Zen
dc.date.available2016-02-25T13:13:59Zen
dc.date.issued2010-06en
dc.identifier.citationDuan R, Fellner K, Zhu C (2010) Energy method for multi-dimensional balance laws with non-local dissipation. Journal de Mathématiques Pures et Appliquées 93: 572–598. Available: http://dx.doi.org/10.1016/j.matpur.2009.10.007.en
dc.identifier.issn0021-7824en
dc.identifier.doi10.1016/j.matpur.2009.10.007en
dc.identifier.urihttp://hdl.handle.net/10754/598168en
dc.description.abstractIn this paper, we are concerned with a class of multi-dimensional balance laws with a non-local dissipative source which arise as simplified models for the hydrodynamics of radiating gases. At first we introduce the energy method in the setting of smooth perturbations and study the stability of constants states. Precisely, we use Fourier space analysis to quantify the energy dissipation rate and recover the optimal time-decay estimates for perturbed solutions via an interpolation inequality in Fourier space. As application, the developed energy method is used to prove stability of smooth planar waves in all dimensions n2, and also to show existence and stability of time-periodic solutions in the presence of the time-periodic source. Optimal rates of convergence of solutions towards the planar waves or time-periodic states are also shown provided initially L1-perturbations. © 2009 Elsevier Masson SAS.en
dc.description.sponsorshipR.-J. Duan would like to thank Prof. Peter Markowich and Dr. Massimo Fornasier for their support during the postdoctoral studies of the year 2008-2009 in RICAM. K. Fellner's work has been supported by the KAUST Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST). The research of C.-J. Zhu was supported by the National Natural Science Foundation of China #10625105 and The Key Laboratory of Mathematical Physics of Hubei Province.en
dc.publisherElsevier BVen
dc.subjectBalance lawsen
dc.subjectEnergy methoden
dc.subjectRate of convergenceen
dc.subjectStabilityen
dc.titleEnergy method for multi-dimensional balance laws with non-local dissipationen
dc.typeArticleen
dc.identifier.journalJournal de Mathématiques Pures et Appliquéesen
dc.contributor.institutionJohann Radon Institute for Computational and Applied Mathematics, Linz, Austriaen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
dc.contributor.institutionHuazhong Normal University, Wuhan, Chinaen
kaust.grant.numberKUK-I1-007-43en
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