The repulsive Euler–Poisson equations with variable doping profile

We prove that arbitrary smooth perturbations of the zero equilibrium state of the repulsive pressureless Euler–Poisson equations, which describe the behavior of cold plasma, blow up for any non-constant doping profile already in one-dimensional space. Further, we study small perturbations of the equ...

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Bibliographic Details
Published in:Physica. D 2025-02, Vol.472, Article 134454
Main Author: Rozanova, Olga S.
Format: Article
Language:English
Subjects:
Equations of cold plasma
Euler–Poisson system
Singularity formation
Variable doping profile
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Summary:We prove that arbitrary smooth perturbations of the zero equilibrium state of the repulsive pressureless Euler–Poisson equations, which describe the behavior of cold plasma, blow up for any non-constant doping profile already in one-dimensional space. Further, we study small perturbations of the equilibrium to determine which properties of the doping profile contribute to the blow-up. We also propose a numerical procedure that allows one to find the blow-up time for any initial data and present examples of such calculations for various doping profiles for standard initial data, corresponding to the laser pulse. •Euler-Poisson system with variable doping: no non-trivial smooth solutions.•Only isochronous oscillatory systems can have smooth solutions.•A numerical procedure that allows one to find the blow-up time is proposed.•A doping profile characteristic responsible for the blow-up is found.
ISSN:0167-2789
DOI:10.1016/j.physd.2024.134454