GLOBAL EXISTENCE OF SOLUTIONS OF CAUCHY PROBLEM FOR GENERALIZED BBM-BURGERS EQUATION

doi:10.1016/S0252-9602(13)60059-4

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (4): 1007-1023.doi: 10.1016/S0252-9602(13)60059-4

GLOBAL EXISTENCE OF SOLUTIONS OF CAUCHY PROBLEM FOR GENERALIZED BBM-BURGERS EQUATION

耿世锋|陈国旺

School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China|Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China

收稿日期:2012-05-24 修回日期:2012-10-26 出版日期:2013-07-20 发布日期:2013-07-20
基金资助:
This work was partially supported by the National Natural Science Foundation of China (11226175, 11271336 and 11171311), Specialized Reseach Fund for the Docotoral Program of Higher Education (20124301120002) and Foundation of He’nan Educational Committee(2009C110006).

GLOBAL EXISTENCE OF SOLUTIONS OF CAUCHY PROBLEM FOR GENERALIZED BBM-BURGERS EQUATION

GENG Shi-Feng, CHEN Guo-Wang

School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China|Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China

Received:2012-05-24 Revised:2012-10-26 Online:2013-07-20 Published:2013-07-20
Supported by:
This work was partially supported by the National Natural Science Foundation of China (11226175, 11271336 and 11171311), Specialized Reseach Fund for the Docotoral Program of Higher Education (20124301120002) and Foundation of He’nan Educational Committee(2009C110006).

摘要/Abstract

摘要：

In this paper, the existence and the uniqueness of the local generalized solution and the local classical solution of the Cauchy problem for the generalized BBM-Burgers equation
v_t − αΔv_t− βΔv + γΔ²v +∑ⁿ_j₌₁f_j (v)x_j = Δg(v) + G(v), x ∈ Rⁿ, t > 0 (1)
are proved. The existence and the uniqueness of the global generalized solution and the global classical solution for the Cauchy problem of equation (1) are proved when n = 3, 2, 1. Moreover, the decay property of the solution is discussed.

关键词: generalized BBM-Burgers equation, Cauchy problem, global solution, decay property of solution

Abstract:

Key words: generalized BBM-Burgers equation, Cauchy problem, global solution, decay property of solution

中图分类号:

35K30

耿世锋, 陈国旺. GLOBAL EXISTENCE OF SOLUTIONS OF CAUCHY PROBLEM FOR GENERALIZED BBM-BURGERS EQUATION[J]. 数学物理学报(英文版), 2013, 33(4): 1007-1023.

GENG Shi-Feng, CHEN Guo-Wang. GLOBAL EXISTENCE OF SOLUTIONS OF CAUCHY PROBLEM FOR GENERALIZED BBM-BURGERS EQUATION[J]. Acta mathematica scientia,Series B, 2013, 33(4): 1007-1023.

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GLOBAL EXISTENCE OF SOLUTIONS OF CAUCHY PROBLEM FOR GENERALIZED BBM-BURGERS EQUATION

GLOBAL EXISTENCE OF SOLUTIONS OF CAUCHY PROBLEM FOR GENERALIZED BBM-BURGERS EQUATION

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