THE INFLUENCE OF NONLOCAL NONLINEARITIES ON THE LONG-TIME BEHAVIOR OF SOLUTIONS OF BURGERS-EQUATION

被引：44

作者：

DENG, K

KWONG, MK

LEVINE, HA

机构：

[1] ARGONNE NATL LAB,ARGONNE,IL 60439

[2] IOWA STATE UNIV SCI & TECHNOL,AMES,IA 50011

来源：

QUARTERLY OF APPLIED MATHEMATICS | 1992年 / 50卷 / 01期

关键词：

D O I：

10.1090/qam/1146631

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the long time behavior of solutions of Burgers's equation with nonlocal nonlinearities: u(t) = u(xx) + epsilon-uu(x) + 1/2 (a parallel-to u(., t)parallel-to p-1 + b)u, 0 < x < 1, a, epsilon is-an-element-of R, b > 0, p > 1, subject to u(0, t) = u(1, t) = 0. A stability-instability analysis is given in some detail, and some finite time blow up results are given.

引用

页码：173 / 200

页数：28

共 50 条

[1] THE LONG-TIME ASYMPTOTICS OF SOLUTIONS TO THE GENERALIZED BURGERS-EQUATION
SCOTT, JF
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1981, 373 (1755): : 443 - 456
[2] ASYMPTOTIC-BEHAVIOR OF SOLUTIONS TO THE BURGERS-EQUATION WITH A NONLOCAL TERM
ITO, K
KAWASHIMA, S
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1994, 23 (12) : 1533 - 1543
[3] BEHAVIOR OF SOLUTIONS OF BURGERS-EQUATION WITH NONLOCAL BOUNDARY-CONDITIONS
DENG, K
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1994, 113 (02) : 394 - 417
[4] LONG-TIME BEHAVIOR OF THE WEAKLY ASYMMETRIC EXCLUSION PROCESS AND THE BURGERS-EQUATION WITHOUT VISCOSITY
DITTRICH, P
[J]. MATHEMATISCHE NACHRICHTEN, 1992, 155 : 279 - 287
[5] LONG-TIME BEHAVIOR OF SOLUTIONS TO A NONLOCAL QUASILINEAR PARABOLIC EQUATION
Le Thi Thuy
Le Tran Tinh
[J]. COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2019, 34 (04): : 1365 - 1388
[6] BEHAVIOR OF SOLUTIONS OF BURGERS-EQUATION WITH NONLOCAL BOUNDARY-CONDITIONS .2.
DENG, K
[J]. QUARTERLY OF APPLIED MATHEMATICS, 1994, 52 (03) : 553 - 567
[7] Long-time behavior for a nonlocal convection diffusion equation
Ignat, Liviu I.
Ignat, Tatiana I.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 455 (01) : 816 - 831
[8] GENERALIZED SOLUTIONS TO BURGERS-EQUATION
BIAGIONI, HA
OBERGUGGENBERGER, M
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1992, 97 (02) : 263 - 287
[9] LONG-TIME, LARGE-SCALE PROPERTIES OF THE RANDOM-FORCE-DRIVEN BURGERS-EQUATION
YAKHOT, V
SHE, ZS
[J]. PHYSICAL REVIEW LETTERS, 1988, 60 (18) : 1840 - 1843
[10] LONG-TIME BEHAVIOR FOR A PLATE EQUATION WITH NONLOCAL WEAK DAMPING
Jorge Silva, M. A.
Narciso, V.
[J]. DIFFERENTIAL AND INTEGRAL EQUATIONS, 2014, 27 (9-10) : 931 - 948

← 1 2 3 4 5 →