TY - JOUR
T1 - Global well-posedness and inviscid limit for the Korteweg-de Vries-Burgers equation
AU - Guo, Zihua
AU - Wang, Baoxiang
PY - 2009
Y1 - 2009
N2 - Considering the Cauchy problem for the Korteweg-de Vries-Burgers equationut + ux x x + ? lunate ?x 2 ? u + (u2)x = 0, u (0) = ? symbol , where 0 <? lunate , ? ? 1 and u is a real-valued function, we show that it is globally well-posed in Hs (s > s?), and uniformly globally well-posed in Hs (s > - 3 / 4) for all ? lunate ? (0, 1]. Moreover, we prove that for any T > 0, its solution converges in C ([0, T] ; Hs) to that of the KdV equation if ? lunate tends to 0.
AB - Considering the Cauchy problem for the Korteweg-de Vries-Burgers equationut + ux x x + ? lunate ?x 2 ? u + (u2)x = 0, u (0) = ? symbol , where 0 <? lunate , ? ? 1 and u is a real-valued function, we show that it is globally well-posed in Hs (s > s?), and uniformly globally well-posed in Hs (s > - 3 / 4) for all ? lunate ? (0, 1]. Moreover, we prove that for any T > 0, its solution converges in C ([0, T] ; Hs) to that of the KdV equation if ? lunate tends to 0.
UR - http://www.sciencedirect.com/science/article/pii/S0022039609001223/pdf?md5=20cc1acadb67c7310799d6a6c8e917cf&pid=1-s2.0-S0022039609001223-main.pdf
U2 - 10.1016/j.jde.2009.03.006
DO - 10.1016/j.jde.2009.03.006
M3 - Article
SN - 0022-0396
VL - 246
SP - 3864
EP - 3901
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 10
ER -