论文标题
关于广义四阶schrödinger方程的溶液的独特性能
On uniqueness properties of solutions of the generalized fourth-order Schrödinger equations
论文作者
论文摘要
在本文中，我们研究了以下形式的任何维度$ d $的通用四阶方程的解决方案的唯一性能，$ i \ partial_t u + + sum_ { \ partial_t u + \ sum_ {j = 1}^d \ partial_ {x_j}^{\，4} u + f（u，\ bar {u}）= 0。$ $我们表明，在两个差异时期，在某些sobolev空间中有足够快的衰减，我们表明了一个线性解决方案$ u $。因此，如果两个非线性解决方案之间的差异$ u_1 $和$ u_2 $在两个不同的时间衰减足够快，则意味着$ u_1 \ equiv U_2 $。
In this paper, we study uniqueness properties of solutions to the generalized fourth-order Schrödinger equations in any dimension $d$ of the following forms, $$i \partial_t u + \sum_{j=1}^d \partial_{x_j}^{\, 4} u = V(t, x) u, \quad \text{and} \quad i \partial_t u + \sum_{j=1}^d \partial_{x_j}^{\, 4} u + F (u, \bar{u}) = 0.$$ We show that a linear solution $u$ with fast enough decay in certain Sobolev spaces at two different times has to be trivial. Consequently, if the difference between two nonlinear solutions $u_1$ and $u_2$ decays sufficiently fast at two different times, it implies that $u_1 \equiv u_2$.
