Periodic initial-value problem for BBM-equation

The BBM or regularized long-wave equation was originally proposed as an alternative to the Korteweg-de Vries equation in describing small-amplitude, long surface wave propagation. Its well-posedness in H1( ) and L2( ) have been studied by many authors. In this paper, I consider the BBM-equation while the initial datais a periodic function on line R. The result is that ifis Lebesgue measurable and square-integrable within one period interval, then equation (0.1) is globally well posed in time t. reserved.