Acta mathematica scientia, Series B >
GLOBAL EXISTENCE OF SOLUTIONS OF CAUCHY PROBLEM FOR GENERALIZED BBM-BURGERS EQUATION
Received date: 2012-05-24
Revised date: 2012-10-26
Online 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).
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
vt − αΔvt − βΔv + γΔ2v +∑nj=1fj (v)xj = 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.
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 . DOI: 10.1016/S0252-9602(13)60059-4
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