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Course by A. T. Il'ichev "Stability of non-uniform states in unbounded spatial domains"
September 9–December 2, 2020, online

Inhomogeneous solutions of partial differential equations describing the dynamics of nonlinear states in unbounded one-dimensional spatial domains, in particular, wave propagation in dispersive and dissipative media, are considered. We study the dynamic stability of these states, both nonlinear (for translationally invariant infinite-dimensional Hamiltonian systems) and spectral (linear). Nonlinear dynamic stability is studied by constructing a Lyapunov function (functional) in Hilbert spaces. Spectral stability is studied by constructing the Evans function – an analytic function in the right complex half-plane of a spectral parameter whose zeros coincide with unstable eigenvalues. Examples from hydrodynamics and elasticity theory are demonstrated.

Financial support. The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2019-1614).

Program

RSS: Forthcoming seminars

Lecturer
Il'ichev Andrej Teimurazovich

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center


Course by A. T. Il'ichev "Stability of non-uniform states in unbounded spatial domains", September 9–December 2, 2020

December 2, 2020 (Wed)
1. Lecture 12. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
December 2, 2020 18:00, online
A. T. Il'ichev
  

November 25, 2020 (Wed)
2. Lecture 11. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
November 25, 2020 18:00, online
A. T. Il'ichev
  

November 18, 2020 (Wed)
3. Lecture 10. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
November 18, 2020 18:00, online
A. T. Il'ichev
  

November 11, 2020 (Wed)
4. Lecture 9. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
November 11, 2020 18:00, online
A. T. Il'ichev
  

October 28, 2020 (Wed)
5. Lecture 8. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
October 28, 2020 18:00, online
A. T. Il'ichev
  

October 21, 2020 (Wed)
6. Lecture 7. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
October 21, 2020 18:00, online
A. T. Il'ichev
  

October 14, 2020 (Wed)
7. Lecture 6. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
October 14, 2020 18:00, online
A. T. Il'ichev
  

October 7, 2020 (Wed)
8. Lecture 5. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
October 7, 2020 18:00, online
A. T. Il'ichev
  

September 30, 2020 (Wed)
9. Lecture 4. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
September 30, 2020 18:00, online
A. T. Il'ichev
  

September 23, 2020 (Wed)
10. Lecture 3. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
September 23, 2020 18:00, online
A. T. Il'ichev
  

September 16, 2020 (Wed)
11. Lecture 2. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
September 16, 2020 18:00, online
A. T. Il'ichev
  

September 9, 2020 (Wed)
12. Lecture 1. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
September 9, 2020 18:00, online
A. T. Il'ichev
  
 
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