Periodic initial-value problem for BBM-Equation

The BBM or regularized long-wave equation [GRAPHICS] was originally proposed as an alternative to the Korteweg-de Vries equation in describing small-amplitude, long surface wave propagation. Its well-posedness in H-1(R) and L-2(R) have been studied by many authors. In this paper, I consider the BBM-equation while the initial data phi is a periodic function on line R. The result is that if phi is Lebesgue measurable and square-integrable within one period interval, then equation (0.1) is globally well posed in time t. (C) 2004 Elsevier Ltd. All rights reserved.