A5015793075- Differential Equations and Boundary Problems
- Advanced Mathematical Modeling in Engineering
- Differential Equations and Numerical Methods
- Stability and Controllability of Differential Equations
- advanced mathematical theories
- Numerical methods in inverse problems
- Vibration and Dynamic Analysis
- Spectral Theory in Mathematical Physics
- Advanced Mathematical Physics Problems
- Advanced Numerical Methods in Computational Mathematics
- Geotechnical and Geomechanical Engineering
- Material Science and Thermodynamics
- Fusion and Plasma Physics Studies
- Composite Material Mechanics
- Medical and Biological Sciences
- Technology and Human Factors in Education and Health
- Algebraic and Geometric Analysis
- Geophysics and Gravity Measurements
- Nonlocal and gradient elasticity in micro/nano structures
- Laser-Matter Interactions and Applications
- Contact Mechanics and Variational Inequalities
- Quantum optics and atomic interactions
- Cold Atom Physics and Bose-Einstein Condensates
- Aquatic and Environmental Studies
- Mathematical functions and polynomials
Lomonosov Moscow State University
2011-2021
Russian Academy of Sciences
2007-2021
Dorodnitsyn Computing Centre
2010-2021
Computing Center
2021
Moscow State University
2008-2015
Russian Customs Academy
2012
Lorestan University
2008-2009
Steklov Mathematical Institute
2000-2007
For a large time interval boundary controls of string vibrations are optimized in the following seven boundary-control problems: displacement control at one end (with other fixed or free); both ends; elastic force combined (displacement and other). Optimal each these problems sought as functions minimizing corresponding boundary-energy integral under constraints from initial terminal conditions for , respectively. all problems, optimal written out closed analytic form.
We define radial multipliers using solutions of the Helmholtz equation, which depend on coordinate, and we find recurrence relations between them in space any dimension m>1, operator is defined. It shown that procedure differentiation these leads to a system represented as products harmonic polynomials. Theorems about properties structure polynomials equation are given. These constructed proposed be used gradient elasticity for multi-layered domains with spherical cylindrical boundaries,...
The nonlocal boundary value problem for the Helmholtz operator in circular sector with equality of flows on radii and to null solution at one radius is considered. conjugated also uniqueness these problems proved built by spectral method.