The simplest parabolic equation of normal type with periodic boundary condition is considered, and the problem of stabilization to zero of its solution with arbitrary initial condition by starting control supported in a prescribed subset is investigated. This problem is reduced to one inequality for starting control, and the proof of this inequality is given. Introduction. This paper is devoted...

We discuss a time-harmonic inverse scattering problem for nonlinear Helmholtz equation with compactly supported inhomogeneous objects that are described by refractive index in unbounded free space. Assuming the knowledge of far field operator, which maps Herglotz incident waves to patterns corresponding solutions problem, we show refraction is uniquely determined. also generalize two reconstruc...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 14 August 2020Accepted: 19 July 2021Published online: 18 October 2021KeywordsHelmholtz equation, limiting-amplitude principle, time integration, indefinite linear systems, solver, preconditionerAMS Subject Headings65N22, 65F10Publication DataISSN (print): 1064-8275ISSN (o...