Axisymmetric solutions of a two-dimensional nonlinear wave system with a two-constant equation of state

We study a special class of Riemann problem with axisymmetry for two-dimensional nonlinear wave equations with the equation of state $p=A_1\rho^{\gamma_1}+A_2\rho^{\gamma_2}$, $A_i<0$, $-3<\gamma_i<-1$ (i=1,2). The main difficulty lies in that the equations can not be directly reduced to an...
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Autor*in:	Guodong Wang [verfasserIn] Yanbo Hu [verfasserIn] Huayong Liu [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2017

Schlagwörter:	Nonlinear wave system generalized Chaplygin gas axisymmetry decoupled system

Übergeordnetes Werk:	In: Electronic Journal of Differential Equations - Texas State University, 2003, (2017), 156,, Seite 18
Übergeordnetes Werk:	year:2017 ; number:156, ; pages:18

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Katalog-ID:	DOAJ032182740

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520			\|a We study a special class of Riemann problem with axisymmetry for two-dimensional nonlinear wave equations with the equation of state $p=A_1\rho^{\gamma_1}+A_2\rho^{\gamma_2}$, $A_i<0$, $-3<\gamma_i<-1$ (i=1,2). The main difficulty lies in that the equations can not be directly reduced to an autonomous system of ordinary differential equations. To solve it, we use the axisymmetry and self-similarity assumptions to reduce the equations to a decoupled system which includes three components of solution. By solving the decoupled system, we obtain the structures of the corresponding solutions and their existence.
650		4	\|a Nonlinear wave system
650		4	\|a generalized Chaplygin gas
650		4	\|a axisymmetry
650		4	\|a decoupled system
653		0	\|a Mathematics
700	0		\|a Yanbo Hu \|e verfasserin \|4 aut
700	0		\|a Huayong Liu \|e verfasserin \|4 aut
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allfields	(DE-627)DOAJ032182740 (DE-599)DOAJ3bbeee02ee1d483cb1d57580a5ad648f DE-627 ger DE-627 rakwb eng QA1-939 Guodong Wang verfasserin aut Axisymmetric solutions of a two-dimensional nonlinear wave system with a two-constant equation of state 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study a special class of Riemann problem with axisymmetry for two-dimensional nonlinear wave equations with the equation of state $p=A_1\rho^{\gamma_1}+A_2\rho^{\gamma_2}$, $A_i<0$, $-3<\gamma_i<-1$ (i=1,2). The main difficulty lies in that the equations can not be directly reduced to an autonomous system of ordinary differential equations. To solve it, we use the axisymmetry and self-similarity assumptions to reduce the equations to a decoupled system which includes three components of solution. By solving the decoupled system, we obtain the structures of the corresponding solutions and their existence. Nonlinear wave system generalized Chaplygin gas axisymmetry decoupled system Mathematics Yanbo Hu verfasserin aut Huayong Liu verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2017), 156,, Seite 18 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2017 number:156, pages:18 https://doaj.org/article/3bbeee02ee1d483cb1d57580a5ad648f kostenfrei http://ejde.math.txstate.edu/Volumes/2017/156/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ 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_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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 AR 2017 156, 18
spelling	(DE-627)DOAJ032182740 (DE-599)DOAJ3bbeee02ee1d483cb1d57580a5ad648f DE-627 ger DE-627 rakwb eng QA1-939 Guodong Wang verfasserin aut Axisymmetric solutions of a two-dimensional nonlinear wave system with a two-constant equation of state 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study a special class of Riemann problem with axisymmetry for two-dimensional nonlinear wave equations with the equation of state $p=A_1\rho^{\gamma_1}+A_2\rho^{\gamma_2}$, $A_i<0$, $-3<\gamma_i<-1$ (i=1,2). The main difficulty lies in that the equations can not be directly reduced to an autonomous system of ordinary differential equations. To solve it, we use the axisymmetry and self-similarity assumptions to reduce the equations to a decoupled system which includes three components of solution. By solving the decoupled system, we obtain the structures of the corresponding solutions and their existence. Nonlinear wave system generalized Chaplygin gas axisymmetry decoupled system Mathematics Yanbo Hu verfasserin aut Huayong Liu verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2017), 156,, Seite 18 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2017 number:156, pages:18 https://doaj.org/article/3bbeee02ee1d483cb1d57580a5ad648f kostenfrei http://ejde.math.txstate.edu/Volumes/2017/156/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ 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_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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 AR 2017 156, 18
allfields_unstemmed	(DE-627)DOAJ032182740 (DE-599)DOAJ3bbeee02ee1d483cb1d57580a5ad648f DE-627 ger DE-627 rakwb eng QA1-939 Guodong Wang verfasserin aut Axisymmetric solutions of a two-dimensional nonlinear wave system with a two-constant equation of state 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study a special class of Riemann problem with axisymmetry for two-dimensional nonlinear wave equations with the equation of state $p=A_1\rho^{\gamma_1}+A_2\rho^{\gamma_2}$, $A_i<0$, $-3<\gamma_i<-1$ (i=1,2). The main difficulty lies in that the equations can not be directly reduced to an autonomous system of ordinary differential equations. To solve it, we use the axisymmetry and self-similarity assumptions to reduce the equations to a decoupled system which includes three components of solution. By solving the decoupled system, we obtain the structures of the corresponding solutions and their existence. Nonlinear wave system generalized Chaplygin gas axisymmetry decoupled system Mathematics Yanbo Hu verfasserin aut Huayong Liu verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2017), 156,, Seite 18 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2017 number:156, pages:18 https://doaj.org/article/3bbeee02ee1d483cb1d57580a5ad648f kostenfrei http://ejde.math.txstate.edu/Volumes/2017/156/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ 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_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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 AR 2017 156, 18
allfieldsGer	(DE-627)DOAJ032182740 (DE-599)DOAJ3bbeee02ee1d483cb1d57580a5ad648f DE-627 ger DE-627 rakwb eng QA1-939 Guodong Wang verfasserin aut Axisymmetric solutions of a two-dimensional nonlinear wave system with a two-constant equation of state 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study a special class of Riemann problem with axisymmetry for two-dimensional nonlinear wave equations with the equation of state $p=A_1\rho^{\gamma_1}+A_2\rho^{\gamma_2}$, $A_i<0$, $-3<\gamma_i<-1$ (i=1,2). The main difficulty lies in that the equations can not be directly reduced to an autonomous system of ordinary differential equations. To solve it, we use the axisymmetry and self-similarity assumptions to reduce the equations to a decoupled system which includes three components of solution. By solving the decoupled system, we obtain the structures of the corresponding solutions and their existence. Nonlinear wave system generalized Chaplygin gas axisymmetry decoupled system Mathematics Yanbo Hu verfasserin aut Huayong Liu verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2017), 156,, Seite 18 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2017 number:156, pages:18 https://doaj.org/article/3bbeee02ee1d483cb1d57580a5ad648f kostenfrei http://ejde.math.txstate.edu/Volumes/2017/156/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ 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_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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 AR 2017 156, 18
allfieldsSound	(DE-627)DOAJ032182740 (DE-599)DOAJ3bbeee02ee1d483cb1d57580a5ad648f DE-627 ger DE-627 rakwb eng QA1-939 Guodong Wang verfasserin aut Axisymmetric solutions of a two-dimensional nonlinear wave system with a two-constant equation of state 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study a special class of Riemann problem with axisymmetry for two-dimensional nonlinear wave equations with the equation of state $p=A_1\rho^{\gamma_1}+A_2\rho^{\gamma_2}$, $A_i<0$, $-3<\gamma_i<-1$ (i=1,2). The main difficulty lies in that the equations can not be directly reduced to an autonomous system of ordinary differential equations. To solve it, we use the axisymmetry and self-similarity assumptions to reduce the equations to a decoupled system which includes three components of solution. By solving the decoupled system, we obtain the structures of the corresponding solutions and their existence. Nonlinear wave system generalized Chaplygin gas axisymmetry decoupled system Mathematics Yanbo Hu verfasserin aut Huayong Liu verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2017), 156,, Seite 18 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2017 number:156, pages:18 https://doaj.org/article/3bbeee02ee1d483cb1d57580a5ad648f kostenfrei http://ejde.math.txstate.edu/Volumes/2017/156/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ 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_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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 AR 2017 156, 18
language	English
source	In Electronic Journal of Differential Equations (2017), 156,, Seite 18 year:2017 number:156, pages:18
sourceStr	In Electronic Journal of Differential Equations (2017), 156,, Seite 18 year:2017 number:156, pages:18
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Nonlinear wave system generalized Chaplygin gas axisymmetry decoupled system Mathematics
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container_title	Electronic Journal of Differential Equations
authorswithroles_txt_mv	Guodong Wang @@aut@@ Yanbo Hu @@aut@@ Huayong Liu @@aut@@
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callnumber-first	Q - Science
author	Guodong Wang
spellingShingle	Guodong Wang misc QA1-939 misc Nonlinear wave system misc generalized Chaplygin gas misc axisymmetry misc decoupled system misc Mathematics Axisymmetric solutions of a two-dimensional nonlinear wave system with a two-constant equation of state
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topic_title	QA1-939 Axisymmetric solutions of a two-dimensional nonlinear wave system with a two-constant equation of state Nonlinear wave system generalized Chaplygin gas axisymmetry decoupled system
topic	misc QA1-939 misc Nonlinear wave system misc generalized Chaplygin gas misc axisymmetry misc decoupled system misc Mathematics
topic_unstemmed	misc QA1-939 misc Nonlinear wave system misc generalized Chaplygin gas misc axisymmetry misc decoupled system misc Mathematics
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title	Axisymmetric solutions of a two-dimensional nonlinear wave system with a two-constant equation of state
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title_sort	axisymmetric solutions of a two-dimensional nonlinear wave system with a two-constant equation of state
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title_auth	Axisymmetric solutions of a two-dimensional nonlinear wave system with a two-constant equation of state
abstract	We study a special class of Riemann problem with axisymmetry for two-dimensional nonlinear wave equations with the equation of state $p=A_1\rho^{\gamma_1}+A_2\rho^{\gamma_2}$, $A_i<0$, $-3<\gamma_i<-1$ (i=1,2). The main difficulty lies in that the equations can not be directly reduced to an autonomous system of ordinary differential equations. To solve it, we use the axisymmetry and self-similarity assumptions to reduce the equations to a decoupled system which includes three components of solution. By solving the decoupled system, we obtain the structures of the corresponding solutions and their existence.
abstractGer	We study a special class of Riemann problem with axisymmetry for two-dimensional nonlinear wave equations with the equation of state $p=A_1\rho^{\gamma_1}+A_2\rho^{\gamma_2}$, $A_i<0$, $-3<\gamma_i<-1$ (i=1,2). The main difficulty lies in that the equations can not be directly reduced to an autonomous system of ordinary differential equations. To solve it, we use the axisymmetry and self-similarity assumptions to reduce the equations to a decoupled system which includes three components of solution. By solving the decoupled system, we obtain the structures of the corresponding solutions and their existence.
abstract_unstemmed	We study a special class of Riemann problem with axisymmetry for two-dimensional nonlinear wave equations with the equation of state $p=A_1\rho^{\gamma_1}+A_2\rho^{\gamma_2}$, $A_i<0$, $-3<\gamma_i<-1$ (i=1,2). The main difficulty lies in that the equations can not be directly reduced to an autonomous system of ordinary differential equations. To solve it, we use the axisymmetry and self-similarity assumptions to reduce the equations to a decoupled system which includes three components of solution. By solving the decoupled system, we obtain the structures of the corresponding solutions and their existence.
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title_short	Axisymmetric solutions of a two-dimensional nonlinear wave system with a two-constant equation of state
url	https://doaj.org/article/3bbeee02ee1d483cb1d57580a5ad648f http://ejde.math.txstate.edu/Volumes/2017/156/abstr.html https://doaj.org/toc/1072-6691
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Axisymmetric solutions of a two-dimensional nonlinear wave system with a two-constant equation of state

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