一类KdV-Burgers型方程的整体适定性

The well-posed problem of the KdV-Burgers type equation.

研究一类KdV-Burgers型方程ut+uxxx+uux+|Dx|2αu=0,t∈R+,x∈R,其中0≤α≤1,在空间Hs(R)上的适定性和不适定性问题.证明了当s>-α时上述方程在空间Hs(R)上是整体适定的,而当s<α-32(2-α)时在空间.Hs(R)上是不适定的.

The well-posedness and ill posedness are considered for the KdV-Burgers type equation ul＋uxxx＋uus＋｜Dx｜^2αu=0,t∈R^＋,x∈R,Where≤α≤1,The equation is well-posedness in H^s（R） when s〉-α,while it＇s illposedness in H^s（R） when s〈α-3/2（2-α）.