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Decay rates of the solutions of nonlinear dispersive equations. (English) Zbl 0814.35115

Summary: We consider a family of dispersive equations whose simplest representative would be a Benjamin-Bona-Mahony equation with a Burger’s type dissipation. The effect of possible unevenness of the bottom surface is considered and our main result gives decay rates of the solutions in \(L^ \beta (\mathbb{R})\) spaces, \(2 \leq \beta \leq + \infty\).

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B40 Asymptotic behavior of solutions to PDEs
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