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Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 8
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Research Article

Global error estimates in zero-relaxation limit of Euler–Poisson system for ion dynamics

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Pages 1498-1512 | Received 29 May 2023, Accepted 27 Aug 2023, Published online: 31 Aug 2023

References

  • Chen F. Introduction to plasma physics and controlled fusion. Vol.1. New York: Plenum Press; 1984.
  • Jüngel A. Quasi-hydrodynamic semiconductor equations, progress in nonlinear differential equations and their applications. Berlin: Birkhäuser; 2001.
  • Guo Y, Pausader B. Global smooth ion dynamics in the Euler–Poisson system. Comm Math Phys. 2011;303:89–125. doi: 10.1007/s00220-011-1193-1
  • Chen GQ, Liu TP. Zero relaxation and dissipation limits for hyperbolic conservation laws. Comm Pure Appl Math. 1993;46(5):755–781. doi: 10.1002/(ISSN)1097-0312
  • Lattanzio C, Yong WA. Hyperbolic-parabolic singular limits for first-order nonlinear systems. Commun Partial Diff Equ. 2001;26:939–964. doi: 10.1081/PDE-100002384
  • Marcati P, Rubino B. Hyperbolic to parabolic relaxation theory for quasilinear first order systems. J Diff Equations. 2000;162:359–399. doi: 10.1006/jdeq.1999.3676
  • Peng YJ, Wasiolek V. Parabolic limit with differential constraints of first-order quasilinear hyperbolic systems. Ann I H Poincaré-AN. 2016;33:1103–1130. doi: 10.4171/aihpc
  • Yong WA. Singular perturbations of first-order hyperbolic systems with stiff source yerms. J Diff Equations. 1999;155:89–132. doi: 10.1006/jdeq.1998.3584
  • Coulombel JF, Goudon T. The strong relaxation limit of the multidimensional isothermal Euler equations. Trans Amer Math Soc. 2007;359:637–648. doi: 10.1090/tran/2007-359-02
  • Marcati P, Milani A. The one-dimensional Darcy's law as the limit of a compressible Euler flow. J Diff Equations. 1990;84:129–147. doi: 10.1016/0022-0396(90)90130-H
  • Hsiao L, Zhang K. The relaxation of the hydrodynamic model for semiconductors to the drift-diffusion equations. J Diff Equations. 2000;165:315–354. doi: 10.1006/jdeq.2000.3780
  • Marcati P, Natalini R. Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation. Arch Rational Mech Anal. 1995;129:129–145. doi: 10.1007/BF00379918
  • Lattanzio C. On the 3-D bipolar isentropic Euler–Poisson model for semiconductors and the drift-diffusion limit. Math Models Methods Appl Sci. 2000;10:351–360. doi: 10.1142/S0218202500000215
  • Alì G, Bini D, Rionero S. Global existence and relaxation limit for smooth solutions to the Euler–Poisson model for semiconductors. SIAM J Math Anal. 2000;32:572–587. doi: 10.1137/S0036141099355174
  • Jüngel A, Peng YJ. A hierarchy of hydrodynamic models for plasmas zero-relaxation-time limits. Comm Part Diff Equations. 1999;24(5–6):1007–1033. doi: 10.1080/03605309908821456.
  • Yong WA. Diffusive relaxation limit of multidimensional isentropic hydrodynamical models for semiconductors. SIAM J Appl Math. 2004;64:1737–1748. doi: 10.1137/S0036139903427404
  • Peng YJ. Uniformly global smooth solutions and convergence of Euler–Poisson systems with small parameters. SIAM J Math Appl. 2015;47:1355–1376. doi: 10.1137/140983276
  • Feng Y, Li X, Wang S. Global zero-relaxation limit of the non-isentropic Euler–Poisson system for ion dynamics. Asymptot Anal. 2020;120(3–4):301–318.
  • Liu CM, Peng YJ. Global convergence of the Euler–Poisson system for ion dynamics. Math Meth Appl Sci. 2019;42(4):1236–1248. doi: 10.1002/mma.v42.4
  • Hajjaj ML, Peng YJ. Initial layers and zero-relaxation limits of multidimensional Euler–Poisson equations. Math Methods Appl Sci. 2013;36:182–195. doi: 10.1002/mma.2580
  • Li Y, Peng YJ, Zhao L. Convergence rate from hyperbolic systems of balance laws to parabolic systems. Appl Anal. 2021;100:1079–1095. doi: 10.1080/00036811.2019.1634258
  • Goudon T, Lin C. Analysis of the M1 model: well-posedness and diffusion asymptotics. J Math Anal Appl. 2013;402:579–593. doi: 10.1016/j.jmaa.2013.01.042
  • Junca S, Rascle M. Strong relaxation of the isothermal Euler system to the heat equation. Z Angew Math Phys. 2002;53:239–264. doi: 10.1007/s00033-002-8154-7
  • Li Y, Peng YJ, Zhao L. Convergence rates in zero-relaxation limits for Euler–Maxwell and Euler–Poisson systems. J Math Pure Appl. 2021;154:185–211. doi: 10.1016/j.matpur.2021.08.011
  • Zhao L, Xi S. Convergence rate from systems of balance laws to isotropic parabolic systems, a periodic case. Asymptot Anal. 2021;124(1–2):163–198.
  • Majda A. Compressible fluid flow and systems of conservation laws in several space variables. New York: Springer-Verlag; 1984.
  • Peng YJ. Stability of non-constant equilibrium solutions for Euler–Maxwell equations. J Math Pure Appl. 2015;103:39–67. doi: 10.1016/j.matpur.2014.03.007
  • Peng YJ, Liu CM. Global quasi-neutral limit for a two-fluid Euler–Poisson system in several space dimensions. SIAM J Math Anal. 2023;55(2):1405–1438. doi: 10.1137/22M1501465

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