Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane

Abstract In the article, a one-dimensional bipolar hydrodynamic model (Euler-Poisson system) in the quarter plane is considered. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. The global existence of smooth small solutions for...
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Autor*in:	Li, Yeping [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2012

Schlagwörter:	bipolar hydrodynamic model nonlinear diffusion waves smooth solutions energy estimates

Übergeordnetes Werk:	Enthalten in: Boundary value problems - Heidelberg : Springer, 2005, 2012(2012), 1 vom: 16. Feb.
Übergeordnetes Werk:	volume:2012 ; year:2012 ; number:1 ; day:16 ; month:02

Links:	Volltext

DOI / URN:	10.1186/1687-2770-2012-21

Katalog-ID:	SPR032694644

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520			\|a Abstract In the article, a one-dimensional bipolar hydrodynamic model (Euler-Poisson system) in the quarter plane is considered. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. The global existence of smooth small solutions for the corresponding initial-boundary value problem is firstly shown. Next, the asymptotic behavior of the solutions towards the nonlinear diffusion waves, which are solutions of the corresponding nonlinear parabolic equation given by the related Darcy's law, is proven. Finally, the optimal convergence rates of the solutions towards the nonlinear diffusion waves are established. The proofs are completed from the energy methods and Fourier analysis. As far as we know, this is the first result about the optimal convergence rates of the solutions of the bipolar Euler-Poisson system with boundary effects towards the nonlinear diffusion waves. Mathematics Subject Classification: 35M20; 35Q35; 76W05.
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allfields	10.1186/1687-2770-2012-21 doi (DE-627)SPR032694644 (SPR)1687-2770-2012-21-e DE-627 ger DE-627 rakwb eng 510 ASE 31.44 bkl 31.45 bkl Li, Yeping verfasserin aut Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In the article, a one-dimensional bipolar hydrodynamic model (Euler-Poisson system) in the quarter plane is considered. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. The global existence of smooth small solutions for the corresponding initial-boundary value problem is firstly shown. Next, the asymptotic behavior of the solutions towards the nonlinear diffusion waves, which are solutions of the corresponding nonlinear parabolic equation given by the related Darcy's law, is proven. Finally, the optimal convergence rates of the solutions towards the nonlinear diffusion waves are established. The proofs are completed from the energy methods and Fourier analysis. As far as we know, this is the first result about the optimal convergence rates of the solutions of the bipolar Euler-Poisson system with boundary effects towards the nonlinear diffusion waves. Mathematics Subject Classification: 35M20; 35Q35; 76W05. bipolar hydrodynamic model (dpeaa)DE-He213 nonlinear diffusion waves (dpeaa)DE-He213 smooth solutions (dpeaa)DE-He213 energy estimates (dpeaa)DE-He213 Enthalten in Boundary value problems Heidelberg : Springer, 2005 2012(2012), 1 vom: 16. Feb. (DE-627)48672557X (DE-600)2187777-4 1687-2770 nnns volume:2012 year:2012 number:1 day:16 month:02 https://dx.doi.org/10.1186/1687-2770-2012-21 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.44 ASE 31.45 ASE AR 2012 2012 1 16 02
spelling	10.1186/1687-2770-2012-21 doi (DE-627)SPR032694644 (SPR)1687-2770-2012-21-e DE-627 ger DE-627 rakwb eng 510 ASE 31.44 bkl 31.45 bkl Li, Yeping verfasserin aut Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In the article, a one-dimensional bipolar hydrodynamic model (Euler-Poisson system) in the quarter plane is considered. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. The global existence of smooth small solutions for the corresponding initial-boundary value problem is firstly shown. Next, the asymptotic behavior of the solutions towards the nonlinear diffusion waves, which are solutions of the corresponding nonlinear parabolic equation given by the related Darcy's law, is proven. Finally, the optimal convergence rates of the solutions towards the nonlinear diffusion waves are established. The proofs are completed from the energy methods and Fourier analysis. As far as we know, this is the first result about the optimal convergence rates of the solutions of the bipolar Euler-Poisson system with boundary effects towards the nonlinear diffusion waves. Mathematics Subject Classification: 35M20; 35Q35; 76W05. bipolar hydrodynamic model (dpeaa)DE-He213 nonlinear diffusion waves (dpeaa)DE-He213 smooth solutions (dpeaa)DE-He213 energy estimates (dpeaa)DE-He213 Enthalten in Boundary value problems Heidelberg : Springer, 2005 2012(2012), 1 vom: 16. Feb. (DE-627)48672557X (DE-600)2187777-4 1687-2770 nnns volume:2012 year:2012 number:1 day:16 month:02 https://dx.doi.org/10.1186/1687-2770-2012-21 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.44 ASE 31.45 ASE AR 2012 2012 1 16 02
allfields_unstemmed	10.1186/1687-2770-2012-21 doi (DE-627)SPR032694644 (SPR)1687-2770-2012-21-e DE-627 ger DE-627 rakwb eng 510 ASE 31.44 bkl 31.45 bkl Li, Yeping verfasserin aut Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In the article, a one-dimensional bipolar hydrodynamic model (Euler-Poisson system) in the quarter plane is considered. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. The global existence of smooth small solutions for the corresponding initial-boundary value problem is firstly shown. Next, the asymptotic behavior of the solutions towards the nonlinear diffusion waves, which are solutions of the corresponding nonlinear parabolic equation given by the related Darcy's law, is proven. Finally, the optimal convergence rates of the solutions towards the nonlinear diffusion waves are established. The proofs are completed from the energy methods and Fourier analysis. As far as we know, this is the first result about the optimal convergence rates of the solutions of the bipolar Euler-Poisson system with boundary effects towards the nonlinear diffusion waves. Mathematics Subject Classification: 35M20; 35Q35; 76W05. bipolar hydrodynamic model (dpeaa)DE-He213 nonlinear diffusion waves (dpeaa)DE-He213 smooth solutions (dpeaa)DE-He213 energy estimates (dpeaa)DE-He213 Enthalten in Boundary value problems Heidelberg : Springer, 2005 2012(2012), 1 vom: 16. Feb. (DE-627)48672557X (DE-600)2187777-4 1687-2770 nnns volume:2012 year:2012 number:1 day:16 month:02 https://dx.doi.org/10.1186/1687-2770-2012-21 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.44 ASE 31.45 ASE AR 2012 2012 1 16 02
allfieldsGer	10.1186/1687-2770-2012-21 doi (DE-627)SPR032694644 (SPR)1687-2770-2012-21-e DE-627 ger DE-627 rakwb eng 510 ASE 31.44 bkl 31.45 bkl Li, Yeping verfasserin aut Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In the article, a one-dimensional bipolar hydrodynamic model (Euler-Poisson system) in the quarter plane is considered. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. The global existence of smooth small solutions for the corresponding initial-boundary value problem is firstly shown. Next, the asymptotic behavior of the solutions towards the nonlinear diffusion waves, which are solutions of the corresponding nonlinear parabolic equation given by the related Darcy's law, is proven. Finally, the optimal convergence rates of the solutions towards the nonlinear diffusion waves are established. The proofs are completed from the energy methods and Fourier analysis. As far as we know, this is the first result about the optimal convergence rates of the solutions of the bipolar Euler-Poisson system with boundary effects towards the nonlinear diffusion waves. Mathematics Subject Classification: 35M20; 35Q35; 76W05. bipolar hydrodynamic model (dpeaa)DE-He213 nonlinear diffusion waves (dpeaa)DE-He213 smooth solutions (dpeaa)DE-He213 energy estimates (dpeaa)DE-He213 Enthalten in Boundary value problems Heidelberg : Springer, 2005 2012(2012), 1 vom: 16. Feb. (DE-627)48672557X (DE-600)2187777-4 1687-2770 nnns volume:2012 year:2012 number:1 day:16 month:02 https://dx.doi.org/10.1186/1687-2770-2012-21 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.44 ASE 31.45 ASE AR 2012 2012 1 16 02
allfieldsSound	10.1186/1687-2770-2012-21 doi (DE-627)SPR032694644 (SPR)1687-2770-2012-21-e DE-627 ger DE-627 rakwb eng 510 ASE 31.44 bkl 31.45 bkl Li, Yeping verfasserin aut Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In the article, a one-dimensional bipolar hydrodynamic model (Euler-Poisson system) in the quarter plane is considered. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. The global existence of smooth small solutions for the corresponding initial-boundary value problem is firstly shown. Next, the asymptotic behavior of the solutions towards the nonlinear diffusion waves, which are solutions of the corresponding nonlinear parabolic equation given by the related Darcy's law, is proven. Finally, the optimal convergence rates of the solutions towards the nonlinear diffusion waves are established. The proofs are completed from the energy methods and Fourier analysis. As far as we know, this is the first result about the optimal convergence rates of the solutions of the bipolar Euler-Poisson system with boundary effects towards the nonlinear diffusion waves. Mathematics Subject Classification: 35M20; 35Q35; 76W05. bipolar hydrodynamic model (dpeaa)DE-He213 nonlinear diffusion waves (dpeaa)DE-He213 smooth solutions (dpeaa)DE-He213 energy estimates (dpeaa)DE-He213 Enthalten in Boundary value problems Heidelberg : Springer, 2005 2012(2012), 1 vom: 16. Feb. (DE-627)48672557X (DE-600)2187777-4 1687-2770 nnns volume:2012 year:2012 number:1 day:16 month:02 https://dx.doi.org/10.1186/1687-2770-2012-21 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.44 ASE 31.45 ASE AR 2012 2012 1 16 02
language	English
source	Enthalten in Boundary value problems 2012(2012), 1 vom: 16. Feb. volume:2012 year:2012 number:1 day:16 month:02
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This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. The global existence of smooth small solutions for the corresponding initial-boundary value problem is firstly shown. Next, the asymptotic behavior of the solutions towards the nonlinear diffusion waves, which are solutions of the corresponding nonlinear parabolic equation given by the related Darcy's law, is proven. Finally, the optimal convergence rates of the solutions towards the nonlinear diffusion waves are established. The proofs are completed from the energy methods and Fourier analysis. As far as we know, this is the first result about the optimal convergence rates of the solutions of the bipolar Euler-Poisson system with boundary effects towards the nonlinear diffusion waves. 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author	Li, Yeping
spellingShingle	Li, Yeping ddc 510 bkl 31.44 bkl 31.45 misc bipolar hydrodynamic model misc nonlinear diffusion waves misc smooth solutions misc energy estimates Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane
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topic_title	510 ASE 31.44 bkl 31.45 bkl Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane bipolar hydrodynamic model (dpeaa)DE-He213 nonlinear diffusion waves (dpeaa)DE-He213 smooth solutions (dpeaa)DE-He213 energy estimates (dpeaa)DE-He213
topic	ddc 510 bkl 31.44 bkl 31.45 misc bipolar hydrodynamic model misc nonlinear diffusion waves misc smooth solutions misc energy estimates
topic_unstemmed	ddc 510 bkl 31.44 bkl 31.45 misc bipolar hydrodynamic model misc nonlinear diffusion waves misc smooth solutions misc energy estimates
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title	Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane
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title_full	Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane
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title_sort	global existence and asymptotic behavior of smooth solutions for a bipolar euler-poisson system in the quarter plane
title_auth	Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane
abstract	Abstract In the article, a one-dimensional bipolar hydrodynamic model (Euler-Poisson system) in the quarter plane is considered. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. The global existence of smooth small solutions for the corresponding initial-boundary value problem is firstly shown. Next, the asymptotic behavior of the solutions towards the nonlinear diffusion waves, which are solutions of the corresponding nonlinear parabolic equation given by the related Darcy's law, is proven. Finally, the optimal convergence rates of the solutions towards the nonlinear diffusion waves are established. The proofs are completed from the energy methods and Fourier analysis. As far as we know, this is the first result about the optimal convergence rates of the solutions of the bipolar Euler-Poisson system with boundary effects towards the nonlinear diffusion waves. Mathematics Subject Classification: 35M20; 35Q35; 76W05.
abstractGer	Abstract In the article, a one-dimensional bipolar hydrodynamic model (Euler-Poisson system) in the quarter plane is considered. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. The global existence of smooth small solutions for the corresponding initial-boundary value problem is firstly shown. Next, the asymptotic behavior of the solutions towards the nonlinear diffusion waves, which are solutions of the corresponding nonlinear parabolic equation given by the related Darcy's law, is proven. Finally, the optimal convergence rates of the solutions towards the nonlinear diffusion waves are established. The proofs are completed from the energy methods and Fourier analysis. As far as we know, this is the first result about the optimal convergence rates of the solutions of the bipolar Euler-Poisson system with boundary effects towards the nonlinear diffusion waves. Mathematics Subject Classification: 35M20; 35Q35; 76W05.
abstract_unstemmed	Abstract In the article, a one-dimensional bipolar hydrodynamic model (Euler-Poisson system) in the quarter plane is considered. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. The global existence of smooth small solutions for the corresponding initial-boundary value problem is firstly shown. Next, the asymptotic behavior of the solutions towards the nonlinear diffusion waves, which are solutions of the corresponding nonlinear parabolic equation given by the related Darcy's law, is proven. Finally, the optimal convergence rates of the solutions towards the nonlinear diffusion waves are established. The proofs are completed from the energy methods and Fourier analysis. As far as we know, this is the first result about the optimal convergence rates of the solutions of the bipolar Euler-Poisson system with boundary effects towards the nonlinear diffusion waves. Mathematics Subject Classification: 35M20; 35Q35; 76W05.
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title_short	Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane
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Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane

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