华东师范大学学报(自然科学版)

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一类无粘性项BBM-Burgers方程解的整体存在性和衰减估计

徐红梅; 徐伟   

  1. 河海大学 理学院, 南京 211100
  • 收稿日期:2015-10-23 出版日期:2016-11-25 发布日期:2017-01-13
  • 通讯作者: 徐红梅, 女, 副教授, 研究方向为偏微分方程. E-mail: xxu_hongmei@163.com.
  • 基金资助:

    国家自然科学基金(11571092)

Global existence and decay estimate of the solution for a BBM-Burgers equation without viscosity

XU Hong-mei, XU Wei   

  1. College of Science, Hohai University, Nanjing 211100, China
  • Received:2015-10-23 Online:2016-11-25 Published:2017-01-13

摘要:

本文通过构造柯西逼近序列证明了一类无粘BBM-Burgers方程解的局部存在性和衰减估计, 应用常数变易公式结合基本解的衰减估计证明了小初值条件下解的整体存在性, 并得到了衰减估计.

关键词: BBM-Burgers方程, 柯西问题, 解的整体存在性, 衰减估计

Abstract:

By constructing a Cauchy approximating sequence, we prove the local existence and give the decay estimate of the solution for a BBM-Burgers equation without viscosity. Using the variation of constant formula and the decay estimate of the fundamental solution, we obtain the global existence and decay estimate of solution of the system with small initial data.

Key words: BBM-Burgers equation, Cauchy problem, global existence of solution, decay estimate