论文标题
标量准电波方程满足弱的无效状态
Modified wave operators for a scalar quasilinear wave equation satisfying the weak null condition
论文作者
论文摘要
我们证明了标量准电波方程满足弱空条件的标量准电波方程的修改波算子的存在。这是通过三个步骤完成的。首先，我们通过修改Hörmander的方法来得出一个新的渐近系统，以用于准电波方程。接下来，我们通过在无限时间解决一些散射数据来解决新的还原系统来构建近似解决方案。最后，我们证明了准电波方程具有一个全局溶液，该解决方案与无限时间的近似解决方案一致。
We prove the existence of the modified wave operators for a scalar quasilinear wave equation satisfying the weak null condition. This is accomplished in three steps. First, we derive a new reduced asymptotic system for the quasilinear wave equation by modifying Hörmander's method. Next, we construct an approximate solution, by solving our new reduced system given some scattering data at infinite time. Finally, we prove that the quasilinear wave equation has a global solution which agrees with the approximate solution at infinite time.
