TY - JOUR

T1 - Evolutionary systems representations based on later time samples and applications to PDEs

AU - Kim, Yeon Hyang

AU - Aceska, Roza

N1 - Funding Information:
This material is based upon work supported by the National Security Agency under Grant No. H98230-18-0144 while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during Summer 2018.
Publisher Copyright:
© 2020 Global-Science Press

PY - 2020/11

Y1 - 2020/11

N2 - Let { fn}∞n=1 be a basis for L2([0, 1]) and {gn}∞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 ∞ u(x, t) = X an fn(x)gn(t), n=1 where an ∈ R, x ∈ [0, 1] and t ∈ [0, ∞), we investigate whether the function f (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 f.

AB - Let { fn}∞n=1 be a basis for L2([0, 1]) and {gn}∞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 ∞ u(x, t) = X an fn(x)gn(t), n=1 where an ∈ R, x ∈ [0, 1] and t ∈ [0, ∞), we investigate whether the function f (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 f.

KW - Dynamical system

KW - Evolutionary systems representation

KW - Initial data

KW - Near-best approximation

KW - PDEs

UR - http://www.scopus.com/inward/record.url?scp=85090888745&partnerID=8YFLogxK

U2 - 10.4208/eajam.210220.120620

DO - 10.4208/eajam.210220.120620

M3 - Article

AN - SCOPUS:85090888745

SN - 2079-7362

VL - 10

SP - 838

EP - 850

JO - East Asian Journal on Applied Mathematics

JF - East Asian Journal on Applied Mathematics

IS - 4

ER -