Acta Mathematica Vietnamica

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Global Existence and Decay Rates of Solutions of Generalized Benjamin–Bona–Mahony Equations in Multiple Dimensions
Hongmei Xu, Guyu Xin

 

Abstract

We study the global existence and decay rates of the Cauchy problem for the generalized Benjamin–Bona–Mahony equations in multi-dimensional spaces. By using Fourier analysis, frequency decomposition, pseudo-differential operators and the energy method, we obtain global existence and optimal L 2 convergence rates of the solution.

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