id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-891	You, Young Hwan	Initial temperature profile recovery under a mixed boundary condition	2024	7	.pdf	application/pdf	2778	166	75	By defining ˆ̄fk = 0 for all k ≥ n+ 1, we obtain ∥f − f̄n∥2 = ∥∥ ∞∑ k=1 (f̂k − ˆ̄fk) sin (2k − 1 2 x )∥∥∥2 L2([0,π]) ≤ C1 ∞∑ k=1 ∣∣f̂k − ˆ̄fk ∣∣2 for some constant C1 ≤ C1 [ n∑ k=1 ∣∣f̂k − ˆ̄fk ∣∣2 + ∞∑ k=n+1 ∣∣f̂k∣∣2] ≤ C1 [ n∑ k=1 ∣∣f̂k − ˆ̄fk ∣∣2 + n−2r ∞∑ k=n+1 (k + 2)2r ∣∣f̂k∣∣2] ≤ C1 [ n∑ k=1 ∣∣∣ ck sin kx0 − c̄k sin kx0 ∣∣∣2 + n−2r ] ≤ C2(t1) n∑ k=1 k2e−4ktk + C1n −2r by (1.7) and Proposition 2.5 ≤ C2(t1) n∑ k=1 k2 e4k(n+k−1)t1 + C1n −2r ≤ C2(t1) e4nt1 n∑ k=1 k2 + C1n −2r ≤ C2(t1) e4nt1 n(n+ 1)(2n+ 1) 6 + C1n −2r EJDE-202X/CONF/27 INITIAL TEMPERATURE PROFILE RECOVERY 103 = C2(t1) [2] A. Aryal, R. Karki; An approach for recovering initial temperature via a bounded linear time sampling, Journal of Mathematical Analysis and Applications, Volume 513, Issue 1, 1 September 2022, 126-179.	cache/ejde-891.pdf	txt/ejde-891.txt