Stability of planar diffusion wave for the three dimensional full bipolar Euler–Poisson system

Yeping Li and Li Lu

Applied Mathematics and Computation, 2019, vol. 356, issue C, 392-410

Abstract: In the paper, we consider a three-dimensional full bipolar classical hydrodynamic model. This model takes the form of non-isentropic bipolar Euler–Poisson with the electric field and the relaxation term added to the momentum equations. Based on the diffusive wave phenomena of the one dimensional full non-isentropic bipolar Euler–Poisson equations, we show the nonlinear stability of the planar diffusive wave for the initial value problem of the three dimensional non-isentropic bipolar Euler–Poisson system. Moreover, the convergence rates in L2-norm and L∞-norm are also obtained. The proofs are finished by some elaborate energy estimates. The study generalizes the result of [Y.-P. Li, J. Differential Equations, 250(2011), 1285–1309] to multi-dimensional case.

Keywords: Bipolar full Euler–Poisson system; Planar diffusion wave; Smooth solution; Energy estimates (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:356:y:2019:i:c:p:392-410

DOI: 10.1016/j.amc.2019.03.019

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