2004/04/23 by A. G. Ramm, А. Г. Рамм, Ramm, A. G.
Engineering · Mathematics · #37C35 #37L05 #37N30 #47A52 #47J06 #65M30 #65N21 #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Functional Analysis (math.FA) #Heat Transfer and Mathematical Modeling #math.FA #msc:37C35 #msc:37L05 #msc:37N30 #msc:47A52 #msc:47J06 #msc:65M30 #msc:65N21
paper · pdf · doi:10.48550/arxiv.math/0404437
arxiv created 2004/04/23 · openalex publication_date 2004/04/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider an operator equation (*) B(u)+\ep u=0 in a real Hilbert space, where \ep>0 is a small constant. The DSM (dynamical systems method) for solving equation (*) consists of a construction of a Cauchy problem, which has the following properties: 1) it has a global solution for an arbitrary initial data, 2) this solution tends to a limit as time tends to infinity, 3) the limit solves the equation B(u)=0. Existence of the unique solution is proved by the DSM for equation (*) with monotone hemicontinuous operators B defined on all of If \ep=0 and equation (**) B(u)=0 is solvable, the DSM yields solution to (**).