On approximating initial data in some linear evolutionary equations involving fraction Laplacian

IF 0.4 Q4 MATHEMATICS, APPLIED Mathematics in applied sciences and engineering Pub Date : 2022-01-19 DOI:10.5206/mase/13511
R. Karki
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Abstract

We study an inverse problem of recovering the intial datum in a one-dimensional linear equation with Dirichlet boundary conditions when finitely many values (samples) of the solution at a suitably fixed space loaction and suitably chosen finitely many later time instances are known. More specifically, we do this. We consider a one-dimentional linear evolutionary equation invliing a Dirichlet fractional Laplacian and the unknown intial datum f that is assumed to be in a suitable subset of a Sovolev space. Then we investigate how to construct a sequence of future times and choose n so that from n samples taken at a suitably fixed space location and the first n terms of the time sequence we can constrcut an approximation to f with the desired accuracy. 
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关于部分拉普拉斯算子线性演化方程中初始数据的逼近
我们研究了一个具有Dirichlet边界条件的一维线性方程的初始数据恢复逆问题,当已知在适当固定的空间位置上的解的有限多个值(样本)和适当选择的有限多稍后的时间实例时。更具体地说,我们这样做。我们考虑了一个一维线性进化方程,该方程包含Dirichlet分数拉普拉斯算子和未知的初始数据f,假设初始数据f在Sovolev空间的合适子集中。然后,我们研究如何构建未来时间序列,并选择n,以便从在适当固定的空间位置采集的n个样本和时间序列的前n项中,我们可以构造出具有所需精度的f的近似值。
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
0
审稿时长
21 weeks
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