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On classical solutions of the relativistic Vlasov-Klein-Gordon system

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We consider a collisionless ensemble of classical particles coupled with a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove local-in-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the p...

We consider a collisionless ensemble of classical particles coupled with a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove local-in-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the particle momenta become large. We also show that classical solutions are global in time in the one-dimensional case. Minimize

Publisher:

Texas State University, Department of Mathematics

Year of Publication:

2005-01-01T00:00:00Z

Document Type:

article

Language:

English

Subjects:

Vlasov equation ; Klein-Gordon equation ; classical solutions. ; LCC:Mathematics ; LCC:QA1-939 ; LCC:Science ; LCC:Q ; DOAJ:Mathematics ; DOAJ:Mathematics and Statistics ; LCC:Mathematics ; LCC:QA1-939 ; LCC:Science ; LCC:Q ; DOAJ:Mathematics ; DOAJ:Mathematics and Statistics ; LCC:Mathematics ; LCC:QA1-939 ; LCC:Science ; LCC:Q ; DOAJ:Mathemati...

Vlasov equation ; Klein-Gordon equation ; classical solutions. ; LCC:Mathematics ; LCC:QA1-939 ; LCC:Science ; LCC:Q ; DOAJ:Mathematics ; DOAJ:Mathematics and Statistics ; LCC:Mathematics ; LCC:QA1-939 ; LCC:Science ; LCC:Q ; DOAJ:Mathematics ; DOAJ:Mathematics and Statistics ; LCC:Mathematics ; LCC:QA1-939 ; LCC:Science ; LCC:Q ; DOAJ:Mathematics ; DOAJ:Mathematics and Statistics ; LCC:Mathematics ; LCC:QA1-939 ; LCC:Science ; LCC:Q ; LCC:Mathematics ; LCC:QA1-939 ; LCC:Science ; LCC:Q Minimize

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Title:

On Classical Solutions of the Relativistic Vlasov-Klein-Gordon System

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We consider a collisionless ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove local-in-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the par...

We consider a collisionless ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove local-in-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the particle momenta become large. We also show that classical solutions are global in time in the one-dimensional case. ; Comment: 18 pages, LaTeX Minimize

Year of Publication:

2004-07-02

Document Type:

text

Subjects:

Mathematics - Analysis of PDEs ; Mathematical Physics ; 35A07 ; 35Q72 ; 35Q40 ; 82C22

Mathematics - Analysis of PDEs ; Mathematical Physics ; 35A07 ; 35Q72 ; 35Q40 ; 82C22 Minimize

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Title:

Global Weak Solutions of the Relativistic Vlasov-Klein-Gordon System

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We consider an ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, which we call the relativistic Vlasov-Klein-Gordon system, we prove the existence of global weak solutions for initial data satisfying a size restriction. The latter becomes necessary since the ene...

We consider an ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, which we call the relativistic Vlasov-Klein-Gordon system, we prove the existence of global weak solutions for initial data satisfying a size restriction. The latter becomes necessary since the energy of the system is indefinite, and only for restricted data a-priori bounds on the solutions can be derived from conservation of energy. ; Comment: Latex, 11 pages, some typos corrected Minimize

Year of Publication:

2002-09-23

Document Type:

text

Subjects:

Mathematics - Analysis of PDEs ; Mathematical Physics ; Primary 35D05 ; 35Q72 ; Secondary 35Q40 ; 82C22

Mathematics - Analysis of PDEs ; Mathematical Physics ; Primary 35D05 ; 35Q72 ; Secondary 35Q40 ; 82C22 Minimize

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Global weak solutions to the relativistic Vlasov-Maxwell system revisited

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Abstract. We consider an ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, which we call the relativistic Vlasov-Klein-Gordon system, we prove the existence of global weak solutions for initial data satisfying a size restriction. The latter becomes necessary sin...

Abstract. We consider an ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, which we call the relativistic Vlasov-Klein-Gordon system, we prove the existence of global weak solutions for initial data satisfying a size restriction. The latter becomes necessary since the energy of the system is indefinite, and only for restricted data a-priori bounds on the solutions can be derived from conservation of energy. 1. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-06

Source:

http://arxiv.org/pdf/math/0209303v1.pdf

http://arxiv.org/pdf/math/0209303v1.pdf Minimize

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text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

Global weak solutions to the relativistic Vlasov-Maxwell system revisited

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Abstract. We consider an ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, which we call the relativistic Vlasov-Klein-Gordon system, we prove the existence of global weak solutions for initial data satisfying a size restriction. The latter becomes necessary sin...

Abstract. We consider an ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, which we call the relativistic Vlasov-Klein-Gordon system, we prove the existence of global weak solutions for initial data satisfying a size restriction. The latter becomes necessary since the energy of the system is indefinite, and only for restricted data a-priori bounds on the solutions can be derived from conservation of energy. 1. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-05

Source:

http://arxiv.org/pdf/math/0209303v2.pdf

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text

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en

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Title:

Global weak solutions to the relativistic Vlasov-Maxwell system revisited

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Abstract. We consider an ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, which we call the relativistic Vlasov-Klein-Gordon system, we prove the existence of global weak solutions for initial data satisfying a size restriction. The latter becomes necessary sin...

Abstract. We consider an ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, which we call the relativistic Vlasov-Klein-Gordon system, we prove the existence of global weak solutions for initial data satisfying a size restriction. The latter becomes necessary since the energy of the system is indefinite, and only for restricted data a-priori bounds on the solutions can be derived from conservation of energy. 1. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-06-15

Source:

http://www.mat.univie.ac.at/%7Egerald/ftp/articles/VlasovKG.pdf

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en

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ftp ejde.math.txstate.edu (login: ftp) ON CLASSICAL SOLUTIONS OF THE RELATIVISTIC VLASOV-KLEIN-GORDON SYSTEM

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Abstract. We consider a collisionless ensemble of classical particles coupled with a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove localin-time existence of classical solutions and a continuation criterion which says that a solution can blow up only...

Abstract. We consider a collisionless ensemble of classical particles coupled with a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove localin-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the particle momenta become large. We also show that classical solutions are global in time in the one-dimensional case. 1. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-06-15

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http://www.mat.univie.ac.at/%7Egerald/ftp/articles/VlasovKG2.pdf

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Title:

On classical solutions of the relativistic Vlasov–Klein–Gordon system

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Abstract. We consider a collisionless ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove localin-time existence of classical solutions and a continuation criterion which says that a solution can blow up only i...

Abstract. We consider a collisionless ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove localin-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the particle momenta become large. We also show that classical solutions are global in time in the one-dimensional case. 1. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-01

Source:

http://arxiv.org/pdf/math/0407028v1.pdf

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Title:

ON CLASSICAL SOLUTIONS OF THE RELATIVISTIC VLASOV-KLEIN-GORDON SYSTEM

Author:

Description:

We consider a collisionless ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove localin-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the part...

We consider a collisionless ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove localin-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the particle momenta become large. We also show that classical solutions are global in time in the one-dimensional case. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-03-06

Source:

http://www.esi.ac.at/preprints/esi1495.pdf

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en

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Title:

2005], On classical solutions of the relativistic Vlasov–Klein–Gordon system

Author:

Description:

Abstract. We consider a collisionless ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove localin-time existence of classical solutions and a continuation criterion which says that a solution can blow up only i...

Abstract. We consider a collisionless ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove localin-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the particle momenta become large. We also show that classical solutions are global in time in the one-dimensional case. 1. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-09-16

Source:

http://www.hyke.org/preprint/2004/13/132.pdf

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en

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