A class of infinite-dimensional dissipative dynamical systems is defined for
which the slow invariant manifolds can be calculated. Large-time behavior of
the evolution of such systems is studied.
A review of the author’s results is given. Inversion formulas and stability results
for the solutions to 3D inverse scattering problems with fixed energy data are obtained. Inversion of exact and noisy data is considered. ...
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier: if Δu = 1 in D ⊂ R[superscript 3], u = 0 on S, the boundary of D, and u[subscript N] = ...
Many three-dimensional manifolds are two-fold branched covers of the three-dimensional sphere. However, there are some that are not. This paper includes exposition about two-fold branched covers and includes many examples. ...
Let q(x) be real-valued compactly supported sufficiently smooth function. It is proved
that the scattering data A(β, α[subscript]0, k) ∀β ∈ S[superscript]2, ∀k > 0, determine q uniquely. Here,
α[subscript]0 ∈ S[superscript]2 ...
Wave scattering problem by many bodies is studied in the case when the bodies are small, ka 1, where a is the characteristic size of a body. The limiting case when a → 0 and the total number of the small bodies is M = ...
Wave scattering by many (M = M(a)) small bodies, at the boundary of which transmission boundary conditions are imposed, is studied. Smallness of the bodies means that ka << 1, where a is the characteristic dimension of the ...
In this paper the author’s invited plenary talk at the 7-th PACOM (Pan African
Congress of Mathematicians), is presented. Asymptotic solution to many-body wave scattering problem is given in the case of many small scatterers. ...