Improved decay rates for solutions for a multidimensional generalized Benjamin–Bona–Mahony equation

Article type: Research Article

Authors: Said-Houari, Belkacem

Affiliations: Division of Mathematical and Computer Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia. E-mail: [email protected]

Abstract: In this paper, we study the decay rates of solutions for the generalized Benjamin–Bona–Mahony equation in multi-dimensional space. For initial data in some L1-weighted spaces, we prove faster decay rates of the solutions. More precisely, using the Fourier transform and the energy method, we show the global existence and the convergence rates of the solutions under the smallness assumption on the initial data and we give better decay rates of the solutions. This result improves early works in J. Differential Equations 158(2) (1999), 314–340 and Nonlinear Anal. 75(7) (2012), 3385–3392.

Keywords: decay of solutions, Benjamin–Bona–Mahony equation, global existence, energy method

DOI: 10.3233/ASY-131191

Journal: Asymptotic Analysis, vol. 86, no. 3-4, pp. 155-164, 2014