TY  - JOUR
A1  - Makhmudo, K. O.
A1  - Makhmudov, O. I.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Equations of Maxwell type
JF  - Journal of mathematical analysis and applications
N2  - For an elliptic complex of first order differential operators on a smooth manifold X, we define a system of two equations which can be thought of as abstract Maxwell equations. The formal theory of this system proves to be very similar to that of classical Maxwell's equations. The paper focuses on boundary value problems for the abstract Maxwell equations, especially on the Cauchy problem.
KW  - Electromagnetic waves
KW  - Scattering
KW  - Elliptic complex
KW  - Green formulas
KW  - Stratton-Chu formulas
KW  - Cauchy problem
Y1  - 2011
U6  - https://doi.org/10.1016/j.jmaa.2011.01.012
SN  - 0022-247X
VL  - 378
IS  - 1
SP  - 64
EP  - 75
PB  - Elsevier
CY  - San Diego
ER  - 
TY  - JOUR
A1  - Glebov, Sergei
A1  - Kiselev, Oleg
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Forced nonlinear resonance in a system of coupled oscillators
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time t similar to s(-2) one component of the system is described for the most part by the inhomogeneous Mathieu equation while the other component represents pulsation of large amplitude. A Hamiltonian system is obtained which describes for the most part the behavior of the envelope in a special case. The analytic results agree with numerical simulations.
Y1  - 2011
U6  - https://doi.org/10.1063/1.3578047
SN  - 1054-1500
VL  - 21
IS  - 2
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Elin, Mark
A1  - Shoikhet, David
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Separation of boundary singularities for holomorphic generators
JF  - Annali di matematica pura ed applicata
N2  - We prove a theorem on separation of boundary null points for generators of continuous semigroups of holomorphic self-mappings of the unit disk in the complex plane. Our construction demonstrates rather strikingly the particular role of the binary operation au broken vertical bar given by 1/ f au broken vertical bar g = 1/f + 1/g on generators.
KW  - Semigroup
KW  - Holomorphic map
KW  - Unit disk
KW  - Angular derivatives
Y1  - 2011
U6  - https://doi.org/10.1007/s10231-010-0165-y
SN  - 0373-3114
VL  - 190
IS  - 4
SP  - 595
EP  - 618
PB  - Springer
CY  - Heidelberg
ER  - 
TY  - JOUR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - The dirichlet to Neumann operator for elliptic complexes
JF  - Transactions of the American Mathematical Society
N2  - We define the Dirichlet to Neumann operator for an elliptic complex of first order differential operators on a compact Riemannian manifold with boundary. Under reasonable conditions the Betti numbers of the complex prove to be completely determined by the Dirichlet to Neumann operator on the boundary.
KW  - Elliptic complexes
KW  - Dirichlet to Neumann operator
KW  - inverse problems
Y1  - 2011
SN  - 0002-9947
VL  - 363
IS  - 12
SP  - 6421
EP  - 6437
PB  - American Mathematical Soc.
CY  - Providence
ER  -