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
Lecturer
Il'ichev Andrej Teimurazovich
Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow Steklov International Mathematical Center |
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Course by A. T. Il'ichev "Stability of non-uniform states in unbounded spatial domains", September 9–December 2, 2020 |
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December 2, 2020 (Wed) |
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Lecture 12. Stability of non-uniform states in unbounded spatial domains A. T. Il'ichev December 2, 2020 18:00, online
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November 25, 2020 (Wed) |
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Lecture 11. Stability of non-uniform states in unbounded spatial domains A. T. Il'ichev November 25, 2020 18:00, online
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November 18, 2020 (Wed) |
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Lecture 10. Stability of non-uniform states in unbounded spatial domains A. T. Il'ichev November 18, 2020 18:00, online
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November 11, 2020 (Wed) |
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Lecture 9. Stability of non-uniform states in unbounded spatial domains A. T. Il'ichev November 11, 2020 18:00, online
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October 28, 2020 (Wed) |
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Lecture 8. Stability of non-uniform states in unbounded spatial domains A. T. Il'ichev October 28, 2020 18:00, online
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October 21, 2020 (Wed) |
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Lecture 7. Stability of non-uniform states in unbounded spatial domains A. T. Il'ichev October 21, 2020 18:00, online
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October 14, 2020 (Wed) |
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Lecture 6. Stability of non-uniform states in unbounded spatial domains A. T. Il'ichev October 14, 2020 18:00, online
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October 7, 2020 (Wed) |
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Lecture 5. Stability of non-uniform states in unbounded spatial domains A. T. Il'ichev October 7, 2020 18:00, online
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September 30, 2020 (Wed) |
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Lecture 4. Stability of non-uniform states in unbounded spatial domains A. T. Il'ichev September 30, 2020 18:00, online
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September 23, 2020 (Wed) |
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Lecture 3. Stability of non-uniform states in unbounded spatial domains A. T. Il'ichev September 23, 2020 18:00, online
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September 16, 2020 (Wed) |
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Lecture 2. Stability of non-uniform states in unbounded spatial domains A. T. Il'ichev September 16, 2020 18:00, online
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September 9, 2020 (Wed) |
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Lecture 1. Stability of non-uniform states in unbounded spatial domains A. T. Il'ichev September 9, 2020 18:00, online
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