Asymptotic behavior of solutions toward the rarefaction waves to the Cauchy problem for the scalar diffusive dispersive conservation laws

被引：4

作者：

Yoshida, Natsumi ^{[1
,2
]}

机构：

[1] Ritsumeikan Univ, OIC Res Org, Ibaraki, Osaka 5678570, Japan

[2] Doshisha Univ, Fac Culture & Informat Sci, Kyotanabe, Kyoto 6100394, Japan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2019年 / 189卷

关键词：

Korteweg-de Vries-Burgers-Kuramoto equation; asymptotic behavior; rarefaction wave; LARGE-TIME BEHAVIOR; MULTIWAVE PATTERN; DECAY PROPERTIES; GLOBAL STABILITY; BURGERS-EQUATION; VRIES EQUATION; MODEL; SYSTEMS; FLUX;

D O I：

10.1016/j.na.2019.111573

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem for the scalar diffusive dispersive conservation laws where the far field states are prescribed. Especially, we deal with the generalized models for Korteweg-de Vries-Burgers-Kuramoto equation. When the corresponding Riemann problem for the hyperbolic part admits a Riemann solution which consists of single rarefaction wave, it is proved that the solution of the Cauchy problem tends toward the rarefaction wave as time goes to infinity. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页数：19

共 50 条

[11] ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE CAUCHY PROBLEM FOR THE SCALAR VISCOUS CONSERVATION LAW WITH PARTIALLY LINEARLY DEGENERATE FLUX
Matsumura, Akitaka
Yoshida, Natsumi
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2012, 44 (04) : 2526 - 2544
[12] Asymptotic Behavior of Solutions Toward a Multiwave Pattern to the Cauchy Problem for the Dissipative Wave Equation with Partially Linearly Degenerate Flux
Yoshida, Natsumi
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 2021, 64 (01): : 49 - 73
[13] ASYMPTOTIC STABILITY OF SOLUTION TO THE INITIAL-BOUNDARY VALUE PROBLEM FOR SCALAR VISCOUS CONSERVATION LAWS CORRESPONDING TO RAREFACTION WAVES
LIU HongXia(Department of Mathematics
SystemsScienceandMathematicalSciences, 1999, (04) : 366 - 377
[14] Asymptotic decay toward the rarefaction waves of solutions for viscous conservation laws in a one-dimensional half space
Nakamura, T
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2003, 34 (06) : 1308 - 1317
[15] GLOBAL ASYMPTOTIC STABILITY OF THE RAREFACTION WAVES TO THE CAUCHY PROBLEM FOR THE GENERALIZED ROSENAU-KORTEWEG-DE VRIES-BURGERS EQUATION
Yoshida, Natsumi
METHODS AND APPLICATIONS OF ANALYSIS, 2023, 30 (01) : 1 - 16
[16] Decay properties of solutions to the Cauchy problem for the scalar conservation law with nonlinearly degenerate viscosity
Yoshida, Natsumi
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 128 : 48 - 76
[17] Nonlinear asymptotic stability in L ∞ for Lipschitz solutions to scalar conservation laws
Golding, William
COMPTES RENDUS MATHEMATIQUE, 2024, 362
[18] Time decay rate of solutions toward the viscous shock waves to the Cauchy problem for the scalar conservation law with nonlinear viscosity and discontinuous initial data
Liu, Yechi
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2022, 222
[19] On the asymptotic behavior of solutions of a singular cauchy problem
Zernov A.E.
Meleshko T.V.
Ukrainian Mathematical Journal, 2001, 53 (9) : 1433 - 1444
[20] Decay properties of solutions toward a multiwave pattern to the Cauchy problem for the scalar conservation law with degenerate flux and viscosity
Yoshida, Natsumi
JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (11) : 7513 - 7558

← 1 2 3 4 5 →