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Asymptotic stability of a nonlinear wave for an outflow problem of the bipolar Navier–Stokes–Poisson system under large initial perturbation.
- Source :
- Zeitschrift für Angewandte Mathematik und Physik (ZAMP); Aug2023, Vol. 74 Issue 4, p1-35, 35p
- Publication Year :
- 2023
-
Abstract
- In this paper, we study the time-asymptotic behavior of solutions to an outflow problem for the one-dimensional bipolar Navier–Stokes–Poisson system in the half space. First, we make some suitable assumptions on the boundary data and space-asymptotic states such that the time-asymptotic state of the solution is a nonlinear wave, which is the superposition of the transonic stationary solution and the 2-rarefaction wave. Next, we show the stability of this nonlinear wave under a class of large initial perturbation, provided that the strength of the transonic stationary solution is small enough, while the amplitude of the 2-rarefaction wave can be arbitrarily large. The proof is completed by a delicate energy method and a continuation argument. The key point is to derive the positive upper and lower bounds of the particle densities. [ABSTRACT FROM AUTHOR]
- Subjects :
- NONLINEAR waves
CONTINUATION methods
NONLINEAR boundary value problems
Subjects
Details
- Language :
- English
- ISSN :
- 00442275
- Volume :
- 74
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
- Publication Type :
- Academic Journal
- Accession number :
- 165112819
- Full Text :
- https://doi.org/10.1007/s00033-023-02029-2