Center manifolds for a class of degenerate evolution equations and existence of small-amplitude kinetic shocks
| Autor: | Kevin Zumbrun, Alin Pogan |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Dynamical systems theory
Applied Mathematics 010102 general mathematics Degenerate energy levels Boundary (topology) 01 natural sciences Boltzmann equation Manifold 010101 applied mathematics symbols.namesake Classical mechanics Flow (mathematics) Boltzmann constant symbols 0101 mathematics Analysis Center manifold Mathematics |
| Zdroj: | Journal of Differential Equations. 264:6752-6808 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2018.01.049 |
| Popis: | We construct center manifolds for a class of degenerate evolution equations including the steady Boltzmann equation and related kinetic models, establishing in the process existence and behavior of small-amplitude kinetic shock and boundary layers. Notably, for Boltzmann's equation, we show that elements of the center manifold decay in velocity at near-Maxwellian rate, in accord with the formal Chapman–Enskog picture of near-equilibrium flow as evolution along the manifold of Maxwellian states, or Grad moment approximation via Hermite polynomials in velocity. Our analysis is from a classical dynamical systems point of view, with a number of interesting modifications to accommodate ill-posedness of the underlying evolution equation. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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