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

摘要

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.