Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions

In this article, we study the initial boundary value problem for nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions $$ u_x(0,t)+\lambda|u(0,t)|^ru(0,t)=0,\quad \lambda\in\mathbb{R}-\{0\},\; r< 0. $$ We discuss the local well-posedness when the initial data $u_0=u(...
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Gespeichert in:

Autor*in:	Ahmet Batal [verfasserIn] Turker Ozsari [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2016

Schlagwörter:	Nonlinear Schrodinger equations nonlinear boundary conditions local well-posedness inhomogeneous boundary conditions

Übergeordnetes Werk:	In: Electronic Journal of Differential Equations - Texas State University, 2003, (2016), 222,, Seite 20
Übergeordnetes Werk:	year:2016 ; number:222, ; pages:20

Links:	Link aufrufen Link aufrufen Journal toc

Katalog-ID:	DOAJ011797118

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allfields	(DE-627)DOAJ011797118 (DE-599)DOAJ73c5f6e6629f44d48cc645eedf1d0989 DE-627 ger DE-627 rakwb eng QA1-939 Ahmet Batal verfasserin aut Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this article, we study the initial boundary value problem for nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions $$ u_x(0,t)+\lambda\|u(0,t)\|^ru(0,t)=0,\quad \lambda\in\mathbb{R}-\{0\},\; r< 0. $$ We discuss the local well-posedness when the initial data $u_0=u(x,0)$ belongs to an $L^2$-based inhomogeneous Sobolev space $H^s(\mathbb{R}_+)$ with $s\in (\frac{1}{2},\frac{7}{2})-\{\frac{3}{2}\}$. We deal with the nonlinear boundary condition by first studying the linear Schrodinger equation with a time-dependent inhomogeneous Neumann boundary condition $u_x(0,t)=h(t)$ where $h\in H^{\frac{2s-1}{4}}(0,T)$. Nonlinear Schrodinger equations nonlinear boundary conditions local well-posedness inhomogeneous boundary conditions Mathematics Turker Ozsari verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2016), 222,, Seite 20 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2016 number:222, pages:20 https://doaj.org/article/73c5f6e6629f44d48cc645eedf1d0989 kostenfrei http://ejde.math.txstate.edu/Volumes/2016/222/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 2016 222, 20
spelling	(DE-627)DOAJ011797118 (DE-599)DOAJ73c5f6e6629f44d48cc645eedf1d0989 DE-627 ger DE-627 rakwb eng QA1-939 Ahmet Batal verfasserin aut Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this article, we study the initial boundary value problem for nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions $$ u_x(0,t)+\lambda\|u(0,t)\|^ru(0,t)=0,\quad \lambda\in\mathbb{R}-\{0\},\; r< 0. $$ We discuss the local well-posedness when the initial data $u_0=u(x,0)$ belongs to an $L^2$-based inhomogeneous Sobolev space $H^s(\mathbb{R}_+)$ with $s\in (\frac{1}{2},\frac{7}{2})-\{\frac{3}{2}\}$. We deal with the nonlinear boundary condition by first studying the linear Schrodinger equation with a time-dependent inhomogeneous Neumann boundary condition $u_x(0,t)=h(t)$ where $h\in H^{\frac{2s-1}{4}}(0,T)$. Nonlinear Schrodinger equations nonlinear boundary conditions local well-posedness inhomogeneous boundary conditions Mathematics Turker Ozsari verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2016), 222,, Seite 20 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2016 number:222, pages:20 https://doaj.org/article/73c5f6e6629f44d48cc645eedf1d0989 kostenfrei http://ejde.math.txstate.edu/Volumes/2016/222/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 2016 222, 20
allfields_unstemmed	(DE-627)DOAJ011797118 (DE-599)DOAJ73c5f6e6629f44d48cc645eedf1d0989 DE-627 ger DE-627 rakwb eng QA1-939 Ahmet Batal verfasserin aut Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this article, we study the initial boundary value problem for nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions $$ u_x(0,t)+\lambda\|u(0,t)\|^ru(0,t)=0,\quad \lambda\in\mathbb{R}-\{0\},\; r< 0. $$ We discuss the local well-posedness when the initial data $u_0=u(x,0)$ belongs to an $L^2$-based inhomogeneous Sobolev space $H^s(\mathbb{R}_+)$ with $s\in (\frac{1}{2},\frac{7}{2})-\{\frac{3}{2}\}$. We deal with the nonlinear boundary condition by first studying the linear Schrodinger equation with a time-dependent inhomogeneous Neumann boundary condition $u_x(0,t)=h(t)$ where $h\in H^{\frac{2s-1}{4}}(0,T)$. Nonlinear Schrodinger equations nonlinear boundary conditions local well-posedness inhomogeneous boundary conditions Mathematics Turker Ozsari verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2016), 222,, Seite 20 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2016 number:222, pages:20 https://doaj.org/article/73c5f6e6629f44d48cc645eedf1d0989 kostenfrei http://ejde.math.txstate.edu/Volumes/2016/222/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 2016 222, 20
allfieldsGer	(DE-627)DOAJ011797118 (DE-599)DOAJ73c5f6e6629f44d48cc645eedf1d0989 DE-627 ger DE-627 rakwb eng QA1-939 Ahmet Batal verfasserin aut Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this article, we study the initial boundary value problem for nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions $$ u_x(0,t)+\lambda\|u(0,t)\|^ru(0,t)=0,\quad \lambda\in\mathbb{R}-\{0\},\; r< 0. $$ We discuss the local well-posedness when the initial data $u_0=u(x,0)$ belongs to an $L^2$-based inhomogeneous Sobolev space $H^s(\mathbb{R}_+)$ with $s\in (\frac{1}{2},\frac{7}{2})-\{\frac{3}{2}\}$. We deal with the nonlinear boundary condition by first studying the linear Schrodinger equation with a time-dependent inhomogeneous Neumann boundary condition $u_x(0,t)=h(t)$ where $h\in H^{\frac{2s-1}{4}}(0,T)$. Nonlinear Schrodinger equations nonlinear boundary conditions local well-posedness inhomogeneous boundary conditions Mathematics Turker Ozsari verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2016), 222,, Seite 20 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2016 number:222, pages:20 https://doaj.org/article/73c5f6e6629f44d48cc645eedf1d0989 kostenfrei http://ejde.math.txstate.edu/Volumes/2016/222/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 2016 222, 20
allfieldsSound	(DE-627)DOAJ011797118 (DE-599)DOAJ73c5f6e6629f44d48cc645eedf1d0989 DE-627 ger DE-627 rakwb eng QA1-939 Ahmet Batal verfasserin aut Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this article, we study the initial boundary value problem for nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions $$ u_x(0,t)+\lambda\|u(0,t)\|^ru(0,t)=0,\quad \lambda\in\mathbb{R}-\{0\},\; r< 0. $$ We discuss the local well-posedness when the initial data $u_0=u(x,0)$ belongs to an $L^2$-based inhomogeneous Sobolev space $H^s(\mathbb{R}_+)$ with $s\in (\frac{1}{2},\frac{7}{2})-\{\frac{3}{2}\}$. We deal with the nonlinear boundary condition by first studying the linear Schrodinger equation with a time-dependent inhomogeneous Neumann boundary condition $u_x(0,t)=h(t)$ where $h\in H^{\frac{2s-1}{4}}(0,T)$. Nonlinear Schrodinger equations nonlinear boundary conditions local well-posedness inhomogeneous boundary conditions Mathematics Turker Ozsari verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2016), 222,, Seite 20 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2016 number:222, pages:20 https://doaj.org/article/73c5f6e6629f44d48cc645eedf1d0989 kostenfrei http://ejde.math.txstate.edu/Volumes/2016/222/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 2016 222, 20
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callnumber-first	Q - Science
author	Ahmet Batal
spellingShingle	Ahmet Batal misc QA1-939 misc Nonlinear Schrodinger equations misc nonlinear boundary conditions misc local well-posedness misc inhomogeneous boundary conditions misc Mathematics Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions
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topic_title	QA1-939 Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions Nonlinear Schrodinger equations nonlinear boundary conditions local well-posedness inhomogeneous boundary conditions
topic	misc QA1-939 misc Nonlinear Schrodinger equations misc nonlinear boundary conditions misc local well-posedness misc inhomogeneous boundary conditions misc Mathematics
topic_unstemmed	misc QA1-939 misc Nonlinear Schrodinger equations misc nonlinear boundary conditions misc local well-posedness misc inhomogeneous boundary conditions misc Mathematics
topic_browse	misc QA1-939 misc Nonlinear Schrodinger equations misc nonlinear boundary conditions misc local well-posedness misc inhomogeneous boundary conditions misc Mathematics
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title	Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions
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title_full	Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions
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title_sort	nonlinear schrodinger equations on the half-line with nonlinear boundary conditions
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title_auth	Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions
abstract	In this article, we study the initial boundary value problem for nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions $$ u_x(0,t)+\lambda\|u(0,t)\|^ru(0,t)=0,\quad \lambda\in\mathbb{R}-\{0\},\; r< 0. $$ We discuss the local well-posedness when the initial data $u_0=u(x,0)$ belongs to an $L^2$-based inhomogeneous Sobolev space $H^s(\mathbb{R}_+)$ with $s\in (\frac{1}{2},\frac{7}{2})-\{\frac{3}{2}\}$. We deal with the nonlinear boundary condition by first studying the linear Schrodinger equation with a time-dependent inhomogeneous Neumann boundary condition $u_x(0,t)=h(t)$ where $h\in H^{\frac{2s-1}{4}}(0,T)$.
abstractGer	In this article, we study the initial boundary value problem for nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions $$ u_x(0,t)+\lambda\|u(0,t)\|^ru(0,t)=0,\quad \lambda\in\mathbb{R}-\{0\},\; r< 0. $$ We discuss the local well-posedness when the initial data $u_0=u(x,0)$ belongs to an $L^2$-based inhomogeneous Sobolev space $H^s(\mathbb{R}_+)$ with $s\in (\frac{1}{2},\frac{7}{2})-\{\frac{3}{2}\}$. We deal with the nonlinear boundary condition by first studying the linear Schrodinger equation with a time-dependent inhomogeneous Neumann boundary condition $u_x(0,t)=h(t)$ where $h\in H^{\frac{2s-1}{4}}(0,T)$.
abstract_unstemmed	In this article, we study the initial boundary value problem for nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions $$ u_x(0,t)+\lambda\|u(0,t)\|^ru(0,t)=0,\quad \lambda\in\mathbb{R}-\{0\},\; r< 0. $$ We discuss the local well-posedness when the initial data $u_0=u(x,0)$ belongs to an $L^2$-based inhomogeneous Sobolev space $H^s(\mathbb{R}_+)$ with $s\in (\frac{1}{2},\frac{7}{2})-\{\frac{3}{2}\}$. We deal with the nonlinear boundary condition by first studying the linear Schrodinger equation with a time-dependent inhomogeneous Neumann boundary condition $u_x(0,t)=h(t)$ where $h\in H^{\frac{2s-1}{4}}(0,T)$.
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title_short	Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions
url	https://doaj.org/article/73c5f6e6629f44d48cc645eedf1d0989 http://ejde.math.txstate.edu/Volumes/2016/222/abstr.html https://doaj.org/toc/1072-6691
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up_date	2024-07-03T22:16:04.462Z
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Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions

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