TY  - INPR
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Mixed problems with a parameter
N2  - Let X be a smooth n -dimensional manifold and D be an open connected set in X with smooth boundary ∂D. Perturbing the Cauchy problem for an elliptic system Au = f in D with data on a closed set Γ ⊂ ∂D we obtain a family of mixed problems depending on a small parameter ε > 0. Although the mixed problems are subject to a non-coercive boundary condition on ∂D\Γ in general, each of them is uniquely solvable in an appropriate Hilbert space DT and the corresponding family {uε} of solutions approximates the solution of the Cauchy problem in DT whenever the solution exists. We also prove that the existence of a solution to the Cauchy problem in DT is equivalent to the boundedness of the family {uε}. We thus derive a solvability condition for the Cauchy problem and an effective method of constructing its solution. Examples for Dirac operators in the Euclidean space Rn are considered. In the latter case we obtain a family of mixed boundary problems for the Helmholtz equation.
T3  - Preprint - (2004) 02 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26677
ER  - 
TY  - INPR
A1  - Berman, Gennady
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Quantum dynamics in the Fermi-Pasta-Ulam problem
N2  - We study the dynamics of four wave interactions in a nonlinear quantum chain of oscillators under the "narrow packet" approximation. We determine the set of times for which the evolution of decay processes is essentially specified by quantum effects. Moreover, we highlight the quantum increment of instability.
T3  - Preprint - (2004) 05 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26695
ER  - 
TY  - INPR
A1  - Kytmanov, Aleksandr
A1  - Myslivets, Simona
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Power sums of roots of a nonlinear system
N2  - For a system of meromorphic functions f = (f1, . . . , fn) in Cn, an explicit formula is given for evaluating negative power sums of the roots of the nonlinear system f(z) = 0.
T3  - Preprint - (2004) 18 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26788
ER  - 
TY  - INPR
A1  - Kytmanov, Aleksandr
A1  - Myslivets, Simona
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Zeta-function of a nonlinear system
N2  - Given a system of entire functions in Cn with at most countable set of common zeros, we introduce the concept of zeta-function associated with the system. Under reasonable assumptions on the system, the zeta-function is well defined for all s ∈ Zn with sufficiently large components. Using residue theory we get an integral representation for the zeta-function which allows us to construct an analytic extension of the zeta-function to an infinite cone in Cn.
T3  - Preprint - (2004) 19 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26795
ER  - 
TY  - INPR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Harmonic integrals on domains with edges
N2  - We study the Neumann problem for the de Rham complex in a bounded domain of Rn with singularities on the boundary. The singularities may be general enough, varying from Lipschitz domains to domains with cuspidal edges on the boundary. Following Lopatinskii we reduce the Neumann problem to a singular integral equation of the boundary. The Fredholm solvability of this equation is then equivalent to the Fredholm property of the Neumann problem in suitable function spaces. The boundary integral equation is explicitly written and may be treated in diverse methods. This way we obtain, in particular, asymptotic expansions of harmonic forms near singularities of the boundary.
T3  - Preprint - (2004) 20 
KW  - domains with singularities
KW  - de Rham complex
KW  - Neumann problem
KW  - Hodge theory
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26800
ER  - 
TY  - INPR
A1  - Gauthier, Paul M.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A covering property of the Riemann zeta-function
N2  - For each compact subset K of the complex plane C which does not surround zero, the Riemann surface Sζ of the Riemann zeta function restricted to the critical half-strip 0 < Rs < 1/2 contains infinitely many schlicht copies of K lying ‘over’ K. If Sζ also contains at least one such copy, for some K which surrounds zero, then the Riemann hypothesis fails.
T3  - Preprint - (2004) 03 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26683
ER  -