Periodic initial-value problem for BBM-equation
The BBM or regularized long-wave equation ut+ux+uux-uxxt=0,x∈ℝ, t>0,u(x,0)=φ(x),x∈ℝ, 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(ℝ) and L2(ℝ) 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. © 2004 Elsevier Ltd. All rights reserved.
Computers and Mathematics with Applications
Chen, H. (2004). Periodic initial-value problem for BBM-equation. Computers and Mathematics with Applications, 48 (9), 1305-1318. https://doi.org/10.1016/j.camwa.2004.10.023