非齐次Burgers方程周期解的大时间行为

数学物理学报 ›› 2015, Vol. 35 ›› Issue (1): 1-14.

• 论文 • 下一篇

非齐次Burgers方程周期解的大时间行为

匡杰¹|王泽军²

1.复旦大学数学科学学院上海 200433;
2.南京航空航天大学数学学系南京 211106

收稿日期:2013-06-13 修回日期:2014-11-25 出版日期:2015-02-25 发布日期:2015-02-25
基金资助:
国家自然科学基金(11031001, 111211101)、国家自然科学基金青年基金(10901082)和中国博士后基金(20090450149) 资助.

The Large Time Behavior of Inhomogeneous Burgers Equation with Periodic Initial Data

Kuang Jie¹|Wang Zejun²

1.School of Mathematics Sciences, Fudan University, Shanghai 200433;
2.Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106

Received:2013-06-13 Revised:2014-11-25 Online:2015-02-25 Published:2015-02-25
Supported by:
国家自然科学基金(11031001, 111211101)、国家自然科学基金青年基金(10901082)和中国博士后基金(20090450149) 资助.

摘要/Abstract

摘要：

研究非齐次 Burgers 方程 Cauchy问题解的大时间行为. 假定初值是周期的并且非齐次项具有多个零点. 对初值的某些假定条件下, 证明了
问题的解收敛于一个行波解. 所用的主要方法是广义特征线理论.

关键词: 非齐次Burgers 方程, 周期性, 行波解, 大时间行为, 广义特征线

Abstract:

In this paper, we study the large time behavior of the Cauchy problem for inhomogeneous Burgers equation. The initial data is assumed to be periodic and the source term has several zero points. We show that under some assumptions on the initial data, the solution approaches to a traveling wave. The main method we used is the theory of generalized characteristics generated by Dafermos C M.

Key words: Inhomogeneous Conservation Laws, Traveling waves solution, Large time behavior, Generalized characteristics

中图分类号:

35L67

匡杰,王泽军. 非齐次Burgers方程周期解的大时间行为[J]. 数学物理学报, 2015, 35(1): 1-14.

Kuang Jie,Wang Zejun. The Large Time Behavior of Inhomogeneous Burgers Equation with Periodic Initial Data[J]. Acta mathematica scientia,Series A, 2015, 35(1): 1-14.

参考文献

[1] Dafermos C M. Regularity and large time behavior of solutions of a conservation law without convexity. Proc Roy Edinburgh, 1985, 51: 99--128

[2] Dafermos C M. Characteristics in hyperbolic conservation laws, nonlinear analysis and mechanics. Research Notes in Math, 1977, 1(17): 1--58

[3] Dafermos C M. Generalized characteristics and the structure of solutions of hyperbolic conservation laws. Indinana Univ Math J,
1977, 26: 1097--1119
[4] Dafermos C M. Generalized characteristics in hyperbolic systems of conservation laws. Arch Rational Mech Anal,1989, 107: 128--155
[5] Dafermos C M. Asymptotic behavior of solutions of hyperbolic balance laws//Bardos C, Bessis D. Bifurcation Phenomena in Mathematical Physics.Dordrecht: Reidel Publish Comp, 1979: 521--533

[6] Diperna R J. Decay and asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws. Indinana Univ Math J, 1975, 24: 1047--1071
[7] Fan H T, Jack K H. Large time behavior in inhomogeneous conservation laws. Arch Rational Mech Anal, 1993, 125: 201--216
[8] Filippov A F. Differential equations with discontinuous right hand side. Math sbornik (N S), 1960, 51: 99--128   (English translation: Amer Soc Transl Ser,42(2): 199--231)

[9] Greenberg J M, Tong D D. Decay of periodic solutions of u_t+f(u)_x=0. J Math Anal Appl, 1973,43: 56--71
[10] Smoller J. Shock Waves and Reaction-Diffusion Equations. New York: Springer, 1994
[11] Kruzkov S N. First order quasilinear equations in several independent variables. Mat Sbornik (N S),  1970, 81: 228--255 (English translation: Math USSR-Sbornik,1970, 10: 217--243)

[12] Lax P D. Hyperbolic systems of conservation laws II. Comm Pure Appl Math, 1957, 10: 537--566

[13] Liu T P. Large time behavior of solutions of initial and initial-boundary value problems of a general system of hyperbolic conservation laws. Comm Math Phys, 1977, 55: 163--177
[14] Lyberopoulos A N. Asymptotic oscillations of solutions of scalar conservation laws without convexity in the presence of a linear source filed. J Differential Equations, 1992, 99(2): 342--380
[15] Vol'pert A I. The space BV and quasilinear equations. Mat Sbornik (N S), 1967, 73(English translation: Math USSR-Sbornik, 1967, 2: 225--267)

非齐次Burgers方程周期解的大时间行为

The Large Time Behavior of Inhomogeneous Burgers Equation with Periodic Initial Data

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 14

Metrics

本文评价

推荐阅读 10

[1]	邹霞, 吴事良. 一类具有非线性发生率与时滞的非局部扩散SIR模型的行波解[J]. 数学物理学报, 2018, 38(3): 496-513.
[2]	王琼, 扈培础. 关于整函数零点和周期性的研究[J]. 数学物理学报, 2018, 38(2): 209-214.
[3]	郭庭光, 徐志庭. 带有扩散项和接种的传染病模型的行波解[J]. 数学物理学报, 2017, 37(6): 1129-1147.
[4]	游凌云, 谭激扬, 黎自强, 张汉君. 复合二项对偶模型中的周期性分红问题[J]. 数学物理学报, 2017, 37(4): 751-766.
[5]	娄翠娟, 杨茵. 一类经典趋化性模型行波解的存在性[J]. 数学物理学报, 2015, 35(6): 1044-1058.
[6]	刘健, 连汝续, 钱茂福. 双极Navier-Stokes-Poisson方程整体解的存在性[J]. 数学物理学报, 2014, 34(4): 960-976.
[7]	马满军, 胡建超, 杨道明. 具非线性扩散一般反应系统的行波解存在性[J]. 数学物理学报, 2012, 32(1): 113-125.
[8]	梁飞, 高洪俊. 非局部时滞反应扩散方程行波解的存在性[J]. 数学物理学报, 2011, 31(5): 1273-1281.
[9]	智红燕, 陈勇, 张鸿庆. 广义射影Riccati方程方法与(2+1)维色散长波方程新的精确行波解[J]. 数学物理学报, 2005, 25(7): 956-964.
[10]	刘春平. 一些非线性发展方程的显式行波解[J]. 数学物理学报, 2004, 4(6): 661-668.
[11]	康东升. 一个反应扩散方程的显式波前解与一个平面三次微分系统的全局分析[J]. 数学物理学报, 1998, 18(S1): 1-12.
[12]	杨向群, 刘良欣. 两参数随机游动[J]. 数学物理学报, 1995, 15(4): 361-367.
[13]	李星. 双周期裂纹场的不同材料弹性平面焊接问题[J]. 数学物理学报, 1993, 13(2): 124-132.
[14]	李星. 三维各向同性不同材料带双周期孔洞的弹性焊接混合边值问题[J]. 数学物理学报, 1992, 12(4): 397-406.