Mathematics – Analysis of PDEs
Scientific paper
2011-12-20
Mathematics
Analysis of PDEs
Scientific paper
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 $H^s(\mathbb{R}),$ for $s\geq 0$ and ill-posed if $s< 0.$ The ill-posedness is in the sense that the flow-map cannot be continuous at the origin from $H^s(\mathbb{R})$ to even $\mathcal{D}'(\mathbb{R}).$ 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.
No associations
LandOfFree
On the BBM-Burgers Equation: Well-posedness, Ill-posedness and Long Period Limit does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the BBM-Burgers Equation: Well-posedness, Ill-posedness and Long Period Limit, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the BBM-Burgers Equation: Well-posedness, Ill-posedness and Long Period Limit will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-58379