TY - JOUR T1 - Evolutionary Systems Representations Based on Later Time Samples and Applications to PDEs AU - Hyang Kim , Yeon AU - Aceska , Roza JO - East Asian Journal on Applied Mathematics VL - 4 SP - 838 EP - 850 PY - 2020 DA - 2020/08 SN - 10 DO - http://doi.org/10.4208/eajam.210220.120620 UR - https://global-sci.org/intro/article_detail/eajam/17965.html KW - Dynamical system, evolutionary systems representation, near-best approximation, initial data, PDEs. AB -

Let $\{ƒ_n\}^∞_{n=1}$ be a basis for $L_2([0, 1])$ and $\{g_n\}^∞_{n=1}$ be a system of functions of controlled decay on [0,∞). Considering a function u(x, t) that can be the represented in the form

image.png

where an ∈ R, x ∈ [0, 1] and t ∈ [0,∞), we investigate whether the function ƒ(x) = u(x, 0) can be approximated, in a reasonable sense, by using data u(x0, t1), u(x0, t2),..., u(x0, tN). 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 ƒ .