Asymptotic  stability  of steady state  solutions for the relativistic Euler-Poisson equations

La-Su  Mai; Kaijun Zhang

doi:10.3934/dcds.2016.36.981

Article Contents

2016, Volume 36, Issue 2: 981-1004. Doi: 10.3934/dcds.2016.36.981

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Asymptotic stability of steady state solutions for the relativistic Euler-Poisson equations

La-Su Mai^1, and
Kaijun Zhang^2,

1.
Department of Mathematics, Capital Normal University, Beijing 100048
2.
School of Mathematics and Statistics, Northeast Normal University, Changchun, MO 130024

Received: May 31, 2014

Revised: May 31, 2014

Published: May 2017

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Abstract

Under the conditions of both the initial data being the small perturbation of given steady state solution and the boundary strength being small, the global existence of smooth solution to the initial boundary value problem of the relativistic Euler-Poisson equations is proved. The convergence of the global smooth solution to smooth steady state solution in time exponentially is also obtained when time goes to infinity.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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