四阶Burgers方程的非线性边值-初值问题

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四阶Burgers方程的非线性边值-初值问题张金良¹, 王飞², 王明亮^1,31. 河南科技大学数学与统计学院, 洛阳 471000;
2. 黄河水利职业技术学院, 开封 475004;
3. 兰州大学数学与统计学院, 兰州 730000 The Nonlinear Boundary-initial Value Problem for the Fourth Order Burgers Equation ZHANG Jinliang¹, WANG Fei², WANG Mingliang^1,31. School of Mathematics & Statistics, Henan University of Science & Technology, Luoyang 471000, China;
2. Yellow River Conservancy Technical Institute, Kaifeng 475004, China;
3. School of Mathematics & Statistcs, Lanzhou University, Lanzhou 730000, China

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摘要本文以变阻尼四阶Burgers方程为例，来说明简化的齐次平衡法是构造某些非线性发展方程非线性边值-初值问题非常有用的方法.首先借助于简化的齐次平衡法，推导出变阻尼四阶Burgers方程与四阶线性方程解之间的非线性变换及其逆变换；由此导出一个新的半无限直线上非线性边值-初值问题；最后讨论了五个特殊的变阻尼四阶Burgers方程，得到了这些非线性边值-初值问题的精确解，特别地，得到了柱（球）四阶Burgers方程非线性边值-初值问题的衰减解.

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收稿日期: 2020-02-01

PACS:

O175.2

基金资助:国家自然科学基金（51675161）资助项目.

引用本文:

张金良, 王飞, 王明亮. 四阶Burgers方程的非线性边值-初值问题[J]. 应用数学学报, 2020, 43(6): 1029-1041. ZHANG Jinliang, WANG Fei, WANG Mingliang. The Nonlinear Boundary-initial Value Problem for the Fourth Order Burgers Equation. Acta Mathematicae Applicatae Sinica, 2020, 43(6): 1029-1041.

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