Consider an operator equation F(u)=0 in a Hilbert space H and assume that this equation is solvable. Let us call the problem of solving this equation ill-posed if the operator F â€²(u) is not boundedlyâ€¦ (More)

Let VZu+k2u+k2a~(z)u+V.(a~(~)Vu) = -6(cc-y) inR3, where al(z) ELâ€™(D), a&) E Hâ€™(D), D E R3_ = {z : 13 < 0) is a finite region, aj(Z) = 0 outside of D, j = 1,2, 1 + 02 > 0, al = El. Assume thatâ€¦ (More)

Theory of wave scattering by many small bodies is developed under various assumptions concerning the ratio a d , where a is the characteristic dimension of a small body and d is the distance betweenâ€¦ (More)

Modified Rayleigh conjecture (MRC) in scattering theory is proposed and justified. MRC allows one to develop numerical algorithms for solving direct scattering problems related to acoustic waveâ€¦ (More)

Let u t = âˆ‡ 2 u âˆ’ q(x)u := Lu in D Ã— [0, âˆž), where D âŠ‚ R 3 is a bounded domain with a smooth connected boundary S, and q(x) âˆˆ L 2 (S) is a real-valued function. is the outer normal to S, one can findâ€¦ (More)

The following question is studied and answered: Is it possible to stably approximate f â€² if one knows: 1) f Î´ âˆˆ L âˆž (R) such that f âˆ’ f Î´ < Î´, and 2) f âˆˆ C âˆž (R), f + f â€² â‰¤ c? Here f := sup xâˆˆR |fâ€¦ (More)

The goal of this work is to show that the numerical solution of the obstacle scattering problem based on the modified Rayleigh conjecture (MRC) method is a competitive alternative to the boundaryâ€¦ (More)

by establishing a relation between the limiting behavior for large times of the trajectories of dynamical systems in H and the solutions to equation (1.1) in a real Hilbert space H. We consider aâ€¦ (More)