A5080649937- Navier-Stokes equation solutions
- Advanced Mathematical Physics Problems
- Computational Fluid Dynamics and Aerodynamics
- Advanced Mathematical Modeling in Engineering
- Gas Dynamics and Kinetic Theory
- Nonlinear Waves and Solitons
- Elasticity and Wave Propagation
- Material Science and Thermodynamics
- Geotechnical and Geomechanical Engineering
- Thermoelastic and Magnetoelastic Phenomena
- Stability and Controllability of Differential Equations
- Elasticity and Material Modeling
- Differential Equations and Boundary Problems
- Fluid Dynamics and Turbulent Flows
- Combustion and Detonation Processes
- Differential Equations and Numerical Methods
- Nonlinear Photonic Systems
- Laser-Plasma Interactions and Diagnostics
- Fluid Dynamics and Thin Films
- Plasma and Flow Control in Aerodynamics
- Dynamics and Control of Mechanical Systems
- Solar and Space Plasma Dynamics
- Quantum chaos and dynamical systems
- High-pressure geophysics and materials
- Spectral Theory in Mathematical Physics
Russian Academy of Sciences
2015-2024
Steklov Mathematical Institute
2015-2024
Research Institute of Agriculture of Crimea
1993
This paper is devoted to a study of problems involving the propagation one-dimensional non-linear waves small amplitude in elastic media, using analytic and numerical methods. The equations elasticity theory belong class hyperbolic systems expressing conservation laws. For unique construction solutions it necessary supplement these with terms that make possible adequately describe actual small-scale phenomena, including structure discontinuities arise. behaviour considered two cases: when...
Abstract Discontinuity structures in solutions of a hyperbolic system equations are considered. The has rather general form and, particular, can describe the longitudinal and torsional non-linear waves elastic rods simplest setting also one-dimensional unbounded media. properties discontinuities these have been investigated earlier under assumption that only relations following from conservation laws for momentum angular about axis rod displacement continuity condition hold on...
The stationary structure stability of discontinuous solutions to nonlinear hyperbolic equations describing the propagation quasi-transverse waves with velocities close characteristic ones are studied. A procedure analyze spectral (linear) these is described. main focus analysis special discontinuities, which represented by integral curve connecting two saddle points corresponding states in front and behind discontinuity. This done using properties Evans function, an analytic function on...