一类非均匀介质中多维非线性Schrdinger方程组的初值和初边值问题

The Initial Value Problem and the Initial-Boundary Value Problem of One Class of the System for Multidimensional Nonlinear Schrodinger Equations In Nonhomogeneous Medium

应用积分估计和不动点原理证明了一类非均匀介质中非线性 Schrodinger 方程组初值和初边值部题整体光滑解的存在唯一性,同时也讨论了解的“blow up”问题。

By using the Integra estimations and the fixed point argument, the existence and uniqueness of the global smooth solution for the initial value problem and the initial-boundary value problem of one class of the system of multidimensional nonlinear Schrodinger equations in nonhomogeneous medium havebeen obtaind.The'blow up' problem also has been discussed in this paper.