On the BBM-Burgers Equation: Well-posedness, Ill-posedness and Long Period Limit

2011/12/20 by Brango, Carlos Banquet
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1112.4724

Abstract

In this work we study a dispersive equation with a dissipative term, the Benjamin-Bona-Mahony-Burgers equation. First we prove that the initial value problem for this equation is well-posed in H^s(ℝ), for s≥ 0 and ill-posed if s< 0. The ill-posedness is in the sense that the flow-map cannot be continuous at the origin from H^s(ℝ) to even D'(ℝ). Additionally, we establish an exact theory of convergence of the periodic solutions to the continuous one, in Sobolev spaces, as the period goes to infinity.

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