Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (3): 473-486.

• Articles •     Next Articles

Pointwise Estimates for the Solution to the Multi-Dimensional Generalized BBM-Burgers Equation

 ZHANG Dan-Dan   

  1. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240
  • Received:2013-05-27 Revised:2013-12-20 Online:2014-06-25 Published:2014-06-25
  • Supported by:

    国家自然科学基金(11071162, 11231006, 11171212, 11171213)资助

Abstract:

In this paper, the author focuses on the time-asymptotic behavior of solution for the scalar multi-dimensional generalized BBM-Burgers equation in the whole-space Rn. By using Green's function method combined with Fourier analysis method, the author yields the pointwise estimates of the solution when the initial data is a small perturbation around the constant state u*, (u*≠0). As a corollary, the optimal decay rate in Lp(Rn)(1≤p≤∞) space is obtained.

Key words: BBM-Burgers equation, Green´s function, Optimal decay estimates,  Energy method, Pointwise estimates

CLC Number: 

  • 35B40
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