论文标题
与Riemann-Liouville衍生物的分数Schrodinger方程相关的源识别问题
Time-dependent source identification problem for a fractional Schrodinger equation with the Riemann-Liouville derivative
论文作者
论文摘要
schrödinger方程$ i \ partial_t^ρu（x，x，t）-u_ {xx}（x，x，x，t）= p（x）q（x） + f（x，x，t）$（$ 0 <t \ leq t，\，0 <ρ<1 $），带有riemann-liouville derivative。研究了一个逆问题，其中，与$ u（x，t）$一起，也未知的源函数的时间依赖因子$ p（t）$。为了解决这个反问题，我们将其他条件$ b [u（\ cdot，t）] =ψ（t）$带有任意有限的线性功能$ b $。证明了解决问题的解决方案的存在和唯一定理。获得了稳定的不平等。应用方法使我们能够通过采取$ d^2/dx^2 $来研究类似的问题，一个任意椭圆差的操作员$ a（x，d）$，具有紧凑的逆。
The Schrödinger equation $i \partial_t^ρu(x,t)-u_{xx}(x,t) = p(t)q(x) + f(x,t)$ ( $0<t\leq T, \, 0<ρ<1$), with the Riemann-Liouville derivative is considered. An inverse problem is investigated in which, along with $u(x,t)$, also a time-dependent factor $p(t)$ of the source function is unknown. To solve this inverse problem, we take the additional condition $ B [u (\cdot,t)] = ψ(t) $ with an arbitrary bounded linear functional $ B $. Existence and uniqueness theorem for the solution to the problem under consideration is proved. Inequalities of stability are obtained. The applied method allows us to study a similar problem by taking instead of $d^2/dx^2$ an arbitrary elliptic differential operator $A(x, D)$, having a compact inverse.
