2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56604A linear equation Au=f (1) with a bounded, injective, but not boundedly invertible linear operator in a Hilbert space H is studied. A new approach to solving linear ill-posed problems is proposed. The approach consists of solving a Cauchy problem for a linear equation in H, which is a dynamical system, proving the existence and uniqueness of its global solution u(t), and establishing that u(t) tends to a limit y, as t tends to infinity, and this limit y solves equation (1). The case when f in (1) is given with some error is also studied.Mathematical PhysicsAnalysis of PDEsDynamical SystemsFunctional Analysis47A50, 47B05, 65M30text