@Article{EAJAM-10-838,
author = {Hyang Kim , Yeon and Aceska , Roza},
title = {Evolutionary Systems Representations Based on Later Time Samples and Applications to PDEs},
journal = {East Asian Journal on Applied Mathematics},
year = {2020},
volume = {10},
number = {4},
pages = {838--850},
abstract = {<p style="text-align: justify;">Let $\{ƒ_n\}^∞_{n=1}$&nbsp;be a basis for $L_2([0, 1])$ and $\{g_n\}^∞_{n=1}$&nbsp;be a system of functions of
controlled decay on [0,∞). Considering a function u(x, t) that can be the represented
in the form</p><p style="text-align:center"><img src="http://admin.global-sci.org/uploads/ueditor/image/20200820/1597887230643613.png" title="1597887230643613.png" alt="image.png"/></p><p style="text-align: justify;">where a<sub>n</sub> ∈ R, x ∈ [0, 1] and t ∈ [0,∞), we investigate whether the function <span style="text-align: justify;">ƒ</span>(x) =
u(x, 0) can be approximated, in a reasonable sense, by using data u(x<sub>0</sub>, t<sub>1</sub>), u(x<sub>0</sub>, t<sub>2</sub>),...,
u(x<sub>0</sub>, t<sub>N</sub>). A mathematical framework and efficient computational schemes are developed to determine approximate solutions for various classes of partial differential equations via sampled data by first establishing a near-best approximation of&nbsp;<span style="text-align: justify;">ƒ</span><span style="text-align: justify;"></span> .<br/></p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.210220.120620 },
url = {http://global-sci.org/intro/article_detail/eajam/17965.html}
}