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引用次数: 0
摘要
在 Dirichlet 边界条件下,Aryal 和 Karki(2022 年)研究了一个逆问题,即从一维物体固定位置的已知温度测量值,以及在有界区间内线性增长的有限多次以后的温度测量值,恢复初始温度曲线。本文研究的是诺伊曼边界条件下的问题。也就是说,在这种边界条件下,我们在长度为 π 的体上适当选择一个固定位置 x0,并构建有限多次 tk, k = 1, 2, 3, ., n,这些时间与 k 呈线性增长,且位于 [0, T] 中,这样,只要 f 位于 L2[0, π] 的一个合适子集中,我们就能根据在 x0 和这 n 个时间测量到的温度,以理想的精度恢复初始温度曲线 f(x)。
Recovery of an initial temperature of a one-dimensional body from finite time-observations
Under the Dirichlet boundary setting, Aryal and Karki (2022) studied an inverse problem of recovering an initial temperature profile from known temperature measurements at a fixed location of a one-dimensional body and at linearly growing finitely many later times within a bounded interval. This paper studies the problem under the Neumann boundary conditions. That is, under this boundary setting, we suitably select a fixed location x0 on the body of length π and construct finitely many times tk, k = 1, 2, 3, . . . , n that grow linearly with k and are in [0, T] such that from the temperature measurements taken at x0 and at these n times, we recover the initial temperature profile f(x) with a desired accuracy, provided f is in a suitable subset of L2[0, π].