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Global existence and decay rates of solutions of generalized Benjamin-Bona-Mahony equations in multiple dimensions. (English) Zbl 1302.35117

Summary: 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.

MSC:

35G25 Initial value problems for nonlinear higher-order PDEs
35B40 Asymptotic behavior of solutions to PDEs
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References:

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