论文标题
从进化方程中的动态样本中恢复快速衰减的源术语
Recovery of rapidly decaying source terms from dynamical samples in evolution equations
论文作者
论文摘要
我们分析了从$ h（t）= \ sum_ {j} h_jϕ（t-t_j）χ_ {[t_j，\ infty）}（t）$从功能hilbert空间中初始价值问题的解决方案$ u $的时空样本中恢复$ h（t）= \ sum_ {j} h_j = h_j = \ sum_ {j} h_jϕ（t-t_j）的问题的问题的问题。在$ h $的表达式中，$ h_j $属于希尔伯特空间，而$ ϕ $是一个通用的实价函数，指数衰减为$ \ infty $。采样策略的设计考虑了测量和背景源的存在中的噪声。
We analyze the problem of recovering a source term of the form $h(t)=\sum_{j}h_jϕ(t-t_j)χ_{[t_j, \infty)}(t)$ from space-time samples of the solution $u$ of an initial value problem in a Hilbert space of functions. In the expression of $h$, the terms $h_j$ belong to the Hilbert space, while $ϕ$ is a generic real-valued function with exponential decay at $\infty$. The design of the sampling strategy takes into account noise in measurements and the existence of a background source.
