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Main Authors: Li, Mingjie, Suzuki, Masahiro
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2403.07594
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author Li, Mingjie
Suzuki, Masahiro
author_facet Li, Mingjie
Suzuki, Masahiro
contents The main concern of this paper is to mathematically investigate the formation of a plasma sheath near the surface of nonplanar walls. We study the existence and asymptotic stability of stationary solutions for the nonisentropic Euler-Poisson equations in a domain of which boundary is drawn by a graph, by employing a space weighted energy method. Moreover, the convergence rate of the solution toward the stationary solution is obtained, provided that the initial perturbation belongs to the weighted Sobolev space. Because the domain is the perturbed half space, we first show the time-global solvability of the nonisentropic Euler-Poisson equations, then construct stationary solutions by using the time-global solutions.
format Preprint
id arxiv_https___arxiv_org_abs_2403_07594
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Stability of Stationary Solutions to the Nonisentropic Euler-Poisson System in a Perturbed Half Space
Li, Mingjie
Suzuki, Masahiro
Analysis of PDEs
The main concern of this paper is to mathematically investigate the formation of a plasma sheath near the surface of nonplanar walls. We study the existence and asymptotic stability of stationary solutions for the nonisentropic Euler-Poisson equations in a domain of which boundary is drawn by a graph, by employing a space weighted energy method. Moreover, the convergence rate of the solution toward the stationary solution is obtained, provided that the initial perturbation belongs to the weighted Sobolev space. Because the domain is the perturbed half space, we first show the time-global solvability of the nonisentropic Euler-Poisson equations, then construct stationary solutions by using the time-global solutions.
title Stability of Stationary Solutions to the Nonisentropic Euler-Poisson System in a Perturbed Half Space
topic Analysis of PDEs
url https://arxiv.org/abs/2403.07594