Asymptotic stability of a stationary solution for the bipolar full Euler–Poisson equation in a bounded domain

2022 ◽  
Vol 64 ◽  
pp. 103442
Author(s):  
Yeping Li ◽  
Rui Xu ◽  
Rong Yin
Keyword(s):  
Asymptotic Stability ◽  
Stationary Solution ◽  
Bounded Domain ◽  
Poisson Equation

scholarly journals APPROXIMATE TRANSMISSION CONDITIONS FOR A POISSON PROBLEM AT MID-DIFFUSION

2015 ◽  
Vol 20 (1) ◽  
pp. 53-75 ◽  
Author(s):  
Khaled El-Ghaouti Boutarene
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Analysis ◽  
Error Estimate ◽  
Thin Layer ◽  
Finite Number ◽  
Bounded Domain ◽  
Poisson Equation ◽  
Transmission Conditions ◽  
Variational Equations ◽  
Poisson Problem

This work consists in the asymptotic analysis of the solution of Poisson equation in a bounded domain of RP(P = 2, 3) with a thin layer. We use a method based on hierarchical variational equations to derive an explicitly asymptotic expansion of the solution with respect to the thickness of the thin layer. We determine the first two terms of the expansion and prove the error estimate made by truncating the expansion after a finite number of terms. Next, using the first two terms of the asymptotic expansion, we show that we can model the effect of the thin layer by a problem with transmission conditions of order two.

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