Acta mathematica scientia, Series B >
DEGENERATE BOUNDARY LAYER SOLUTIONS TO THE GENERALIZED BENJAMIN-BONAMAHONY-BURGERS EQUATION
Received date: 2011-07-06
Revised date: 2011-10-12
Online published: 2012-09-20
Supported by
This work was supported by the “Fundamental Research Funds for the Central Universities” and the National Natural Science Foundation of China (10871151).
This paper is concerned with the convergence rates of the global solutions of the generalized Benjamin-Bona-Mahony-Burgers (BBM-Burgers) equation to the cor-responding degenerate boundary layer solutions in the half-space. It is shown that the convergence rate is t−α/4 as t →1 provided that the initial perturbation lies in H1α for α < α(q) := 3+ 2/q , where q is the degeneracy exponent of the flux function. Our analysis is based on the space-time weighted energy method combined with a Hardy type inequality with the best possible constant introduced in [1].
XIAO Qing-Hua , CHEN Zheng-Zheng . DEGENERATE BOUNDARY LAYER SOLUTIONS TO THE GENERALIZED BENJAMIN-BONAMAHONY-BURGERS EQUATION[J]. Acta mathematica scientia, Series B, 2012 , 32(5) : 1743 -1758 . DOI: 10.1016/S0252-9602(12)60138-6
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