Complex-Valued Burgers and KdV-Burgers Equations

被引：2

作者：

Khanal, Netra ^{[1
]}

Wu, Jiahong ^{[2
]}

Yuan, Juan-Ming ^{[3
]}

Zhang, Bing-Yu ^{[4
]}

机构：

[1] Univ Wisconsin Washington Cty, Dept Math, W Bend, WI 53095 USA

[2] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA

[3] Providence Univ, Dept Appl Math, Taichung 433, Taiwan

[4] Univ Cincinnati, Dept Math Sci, Cincinnati, OH 45221 USA

来源：

JOURNAL OF NONLINEAR SCIENCE | 2010年 / 20卷 / 03期

基金：

美国国家科学基金会;

关键词：

Complex Burgers equation; Complex KdV-Burgers equation; Finite-time singularity; Global regularity; DE-VRIES EQUATION; BLOW-UP; DISSIPATION;

D O I：

10.1007/s00332-010-9062-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Spatially periodic complex-valued solutions of the Burgers and KdV-Burgers equations are studied in this paper. It is shown that for any sufficiently large time T, there exists an explicit initial datum such that its corresponding solution of the Burgers equation blows up at T. In addition, the global convergence and regularity of series solutions is established for initial data satisfying mild conditions.

引用

页码：341 / 360

页数：20

共 50 条

[21] Similarity Solutions for the Complex Burgers' Hierarchy
Haider, Amlan K.
Paliathanasis, A.
Rangasamy, S.
Leach, P. G. L.
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2019, 74 (07): : 597 - 604
[22] Inverse optimality of boundary controls for uncertain burgers, KdV and KdVB equation
Cai, Xiushan
Lin, Yuhang
Wang, Ping
Huang, Shuwei
INTERNATIONAL JOURNAL OF CONTROL, 2025,
[23] Singularities and heteroclinic connections in complex-valued evolutionary equations with a quadratic nonlinearity
Jaquette, Jonathan
Lessard, Jean-Philippe
Takayasu, Akitoshi
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2022, 107
[24] Characteristic Study of Head-on Collision of Ion Acoustic Dissipative Solitons in a Ultracold Neutral Plasma Through the Both Sided Damped KdV-Burgers Equation
Jayshree Mondal
Santanu Raut
Prasanta Chatterjee
Laxmikanta Mandi
Brazilian Journal of Physics, 2025, 55 (4)
[25] On the blow-up of solutions of the Benjamin-Bona-Mahony-Burgers and Rosenau-Burgers equations
Korpusov, M. O.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (04) : 1737 - 1743
[26] COMPLEX-VALUED SOLUTIONS OF THE MKDV EQUATIONS IN GENERALIZED FOURIER-LEBESGUE SPACES
Chen, Zijun
Guo, Zihua
Huang, Chunyan
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2025, 153 (04) : 1621 - 1640
[27] On the Cauchy Problem for Dispersive Burgers-Type Equations
Said, Ayman Rimah
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2023, 72 (04) : 1667 - 1715
[28] DISPERSIVE PERTURBATIONS OF BURGERS AND HYPERBOLIC EQUATIONS I: LOCAL THEORY
Linares, Felipe
Pilod, Didier
Saut, Jean-Claude
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2014, 46 (02) : 1505 - 1537
[29] A class of blowup and global analytical solutions of the viscoelastic Burgers' equations
An, Hongli
Cheung, Ka-Luen
Yuen, Manwai
PHYSICS LETTERS A, 2013, 377 (37) : 2275 - 2279
[30] Blow-Up of Solutions to Fractional-in-Space Burgers-Type Equations
Alotaibi, Munirah
Jleli, Mohamed
Samet, Bessem
FRACTAL AND FRACTIONAL, 2021, 5 (04)

← 1 2 3 4 5 →