一类非线性色散波方程的适定性

Well-posedness for a nonlinearly dispersive wave equation

文章主要应用T.Kato’s方法,在加权Soblolev空间H2r,r下研究了一类非线性色散波方程的cauchy问题,得到了解的局部适定性;当r→∞时,在Schwartz空间也有相似的结论。

In this paper, by applying the method of T. Kato, the Cauchy problem is studied for a new nonlinearly dispersive wave equation in weighted Sobolev spaces H^2r,r and the local well posedness of the solution is obtained. The same is true in the Schwartz space P as r →∞.