论文标题
控制与混合色散的Schrödinger型系统解决方案的差异
Controls insensitizing the norm of solution of a Schrödinger type system with mixed dispersion
论文作者
论文摘要
该手稿的主要目的是证明存在具有立方非线性的四阶分散非线性schrödinger方程的不敏感控制。为了获得主要结果，我们证明了耦合的四阶Schrödinger级联类型系统具有零级耦合的零可控性能，该系统等同于不敏感的控制问题。确切地说，采用新的Carleman估计值，我们首先获得了零附近线性化系统的无可控性结果，然后使用反向映射定理扩展了非线性情况的无效可控性。
The main goal of this manuscript is to prove the existence of insensitizing controls for the fourth-order dispersive nonlinear Schrödinger equation with cubic nonlinearity. To obtain the main result we prove a null controllability property for a coupled fourth-order Schrödinger cascade type system with zero-order coupling which is equivalent to the insensitizing control problem. Precisely, employing a new Carleman estimate, we first obtain a null controllability result for the linearized system around zero, and then the null controllability for the nonlinear case is extended using an inverse mapping theorem.
