On an inverse problem for the Steklov spectrum of a Riemannian surface

2014 ◽  
pp. 165-191 ◽  
Author(s):  
Alexandre Jollivet ◽  
Vladimir Sharafutdinov
Keyword(s):  
Inverse Problem ◽  
Riemannian Surface ◽  
Steklov Spectrum

scholarly journals The Steklov spectrum of surfaces: asymptotics and invariants

2014 ◽  
Vol 157 (3) ◽  
pp. 379-389 ◽  
Author(s):  
ALEXANDRE GIROUARD ◽  
LEONID PARNOVSKI ◽  
IOSIF POLTEROVICH ◽  
DAVID A. SHER
Keyword(s):  
Connected Components ◽  
Riemannian Surface ◽  
Precise Asymptotics ◽  
Neumann Operator ◽  
Theoretic Argument ◽  
Steklov Spectrum ◽  
Steklov Eigenvalues ◽  
Dirichlet To Neumann Operator

AbstractWe obtain precise asymptotics for the Steklov eigenvalues on a compact Riemannian surface with boundary. It is shown that the number of connected components of the boundary, as well as their lengths, are invariants of the Steklov spectrum. The proofs are based on pseudodifferential techniques for the Dirichlet-to-Neumann operator and on a number–theoretic argument.

AN INVERSE PROBLEM IN THE DYNAMICAL REATOR THEORY

1982 ◽  
Vol 2 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Dexing Feng ◽  
Guangtian Zhu
Keyword(s):  
Inverse Problem

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

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