Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗

Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗

We consider the generalized Korteweg-de Vries equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the scalar conservation law. The proof relies on deriving...

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Main Authors: Giuseppe Maria Coclite, Lorenzo di Ruvo
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2016-03-01
Series:Mathematical Modelling and Analysis
Subjects:
singular limit
compensated compactness
connected compactness
Korteweg-de Vries equation
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/808
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spelling doaj-5017468a15454e52b9faacb8beaab9392021-07-02T11:45:12ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102016-03-0121210.3846/13926292.2016.1150358Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗Giuseppe Maria Coclite0Lorenzo di Ruvo1Department of Mathematics, University of Bari via E. Orabona 4, 70125 Bari, ItalyDepartment of Science and Methods for Engineering, University of Modena and Reggio Emilia via G. Amendola 2, 42122 Reggio Emilia, Italy We consider the generalized Korteweg-de Vries equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the Lp setting. https://journals.vgtu.lt/index.php/MMA/article/view/808singular limitcompensated compactnessconnected compactnessKorteweg-de Vries equation
collection DOAJ
language English
format Article
sources DOAJ
author Giuseppe Maria Coclite
Lorenzo di Ruvo
spellingShingle Giuseppe Maria Coclite
Lorenzo di Ruvo
Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗
Mathematical Modelling and Analysis
singular limit
compensated compactness
connected compactness
Korteweg-de Vries equation
author_facet Giuseppe Maria Coclite
Lorenzo di Ruvo
author_sort Giuseppe Maria Coclite
title Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗
title_short Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗
title_full Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗
title_fullStr Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗
title_full_unstemmed Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗
title_sort convergence of the solutions on the generalized korteweg–de vries equation∗
publisher Vilnius Gediminas Technical University
series Mathematical Modelling and Analysis
issn 1392-6292
1648-3510
publishDate 2016-03-01
description We consider the generalized Korteweg-de Vries equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the Lp setting.
topic singular limit
compensated compactness
connected compactness
Korteweg-de Vries equation
url https://journals.vgtu.lt/index.php/MMA/article/view/808
work_keys_str_mv AT giuseppemariacoclite convergenceofthesolutionsonthegeneralizedkortewegdevriesequation
AT lorenzodiruvo convergenceofthesolutionsonthegeneralizedkortewegdevriesequation
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