Convergence of the Solutions on the Generalized Korteweg-de Vries Equation

被引：13

作者：

Coclite, Giuseppe Maria ^{[1
]}

di Ruvo, Lorenzo ^{[2
]}

机构：

[1] Univ Bari, Dept Math, Via E Orabona 4, I-70125 Bari, Italy

[2] Univ Modena & Reggio Emilia, Dept Sci & Methods Engn, Via G Amendola 2, I-42122 Reggio Emilia, Italy

来源：

MATHEMATICAL MODELLING AND ANALYSIS | 2016年 / 21卷 / 02期

关键词：

compensated compactness; singular limit; Korteweg-de Vries equation; connected compactness; 35L65; 35L05; 35G25; CONSERVATION-LAWS; DIFFUSION; DISPERSION; ENTROPY; LIMIT;

D O I：

10.3846/13926292.2016.1150358

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 L-p setting.

引用

页码：239 / 259

页数：21

共 50 条

[1] Classical Solutions for the Generalized Korteweg-de Vries Equation
Georgiev, Svetlin
Boukarou, Aissa
Hajjej, Zayd
Zennir, Khaled
[J]. AXIOMS, 2023, 12 (08)
[2] Similarity solutions of the generalized Korteweg-de Vries equation
Bona, JL
Weissler, FB
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1999, 127 : 323 - 351
[3] GENERALIZED KORTEWEG-DE VRIES EQUATION
TSUTSUMI, M
MUKASA, T
IINO, R
[J]. PROCEEDINGS OF THE JAPAN ACADEMY, 1970, 46 (09): : 921 - &
[4] ON THE (GENERALIZED) KORTEWEG-DE VRIES EQUATION
KENIG, CE
PONCE, G
VEGA, L
[J]. DUKE MATHEMATICAL JOURNAL, 1989, 59 (03) : 585 - 610
[5] Rapidly oscillating solutions of a generalized Korteweg-de Vries equation
Kashchenko, S. A.
[J]. COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2017, 57 (11) : 1778 - 1788
[6] Wronskians, generalized Wronskians and solutions to the Korteweg-de Vries equation
Ma, WX
[J]. CHAOS SOLITONS & FRACTALS, 2004, 19 (01) : 163 - 170
[7] On the Generalized Nonlinear Korteweg-De Vries Equation
Gladkov, S. O.
[J]. TECHNICAL PHYSICS, 2024,
[8] Bifurcations in the Generalized Korteweg-de Vries Equation
Kashchenko, S. A.
Preobrazhenskaya, M. M.
[J]. RUSSIAN MATHEMATICS, 2018, 62 (02) : 49 - 61
[9] Convergence of the Rosenau-Korteweg-de Vries Equation to the Korteweg-de Vries One
Coclite, Giuseppe Maria
di Ruvo, Lorenzo
[J]. CONTEMPORARY MATHEMATICS, 2020, 1 (05): : 365 - 392
[10] SOLUTION OF A GENERALIZED KORTEWEG-DE VRIES EQUATION
TAGARE, SG
CHAKRABARTI, A
[J]. PHYSICS OF FLUIDS, 1974, 17 (06) : 1331 - 1332

← 1 2 3 4 5 →