id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6559	Alshanti, Waseem; Abu Hammad, Ma'mon; Khalil, Roshdi	Second-Order Abstract Cauchy Problem in Two Variables	2025	8	.pdf	application/pdf	2999	207	76	Math, 18 (4) (2025), 6559 5 of 8 Therefore, for all ω ̸= 0 ∈ X, an atomic solution, of the form u = P ⊗Q ⊗ ω to (2), can be obtained, by considering (9) and (11), as u(s, t) Math, 18 (4) (2025), 6559 2 of 8 where L : Dom(L) ⊆ X → X is a linear operator of an appropriate type such that Rang(u) ⊆ Dom(L), t◦ ∈ X is given and u : [0,∞) → X is the unknown function.	cache/ejpam-6559.pdf	txt/ejpam-6559.txt