id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5386	Tatar, Salih; BenSalah, Mohamed ; Alamil, Maryam	Simultaneous Identification of the Parameters in the Mathematical Model of Brain Tumor Growth Dynamics Under Treatment	2024	25	.pdf	application/pdf	8808	491	63	Math, 17 (4) (2024), 2651-2675 2655 Here the inverse problem consists of simultaneously determining the treatment profile k(x, t) and the initial tumor cell density φ, by means of the time-integral measurements of tumor cell density (measured data) defined as follows: ϕ1 := ∫ T 0 ω1(t) c(x, t) dt and ϕ2 := ∫ T 0 ω2(t) c(x, t) dt, x ∈ B, (3) where ω1(t) and ω2(t) denote two distinct weight functions. We note that since time- integral measurements of tumor cell density do not typically reveal time-dependent profiles, we consider the function k(x, t) ∈ L∞(Q) in the following separable form: k(x, t) = α(x)β(t), (4) where α(x) ∈ L∞(B) represents the spatial component of the treatment profile k(x, t) and describes how the treatment efficacy varies across different spatial locations within the brain region.	cache/ejpam-5386.pdf	txt/ejpam-5386.txt