The Time Decay Rates of the Classical Solution to the Poisson-Nernst-Planck-Fourier Equations in ℝ3

被引：0
作者：
Leilei Tong
Zhong Tan
Xu Zhang
机构：
[1] Chongqing University of Posts and Telecommunications,School of Science
[2] Xiamen University,School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing
[3] Zhengzhou University,School of Mathematics and Statistics
来源：
Acta Mathematica Scientia | 2022年 / 42卷
关键词：
Poisson-Nernst-Planck-Fourier system; decay rates; energy method; 35Q70; 35Q92; 82C21; 35Q79;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this work, the Poisson-Nernst-Planck-Fourier system in three dimensions is considered. For when the initial data regards a small perturbation around the constant equilibrium state in a H3 ∩ Ḣ−s (0 ≤ s ≤ 1/2) norm, we obtain the time convergence rate of the global solution by a regularity interpolation trick and an energy method.
引用
收藏
页码：1081 / 1102
页数：21
相关论文
共 89 条
  • [1] Barcilon V(1997)Qualitative properties of steady-state Poisson-Nernst-Planck systems: perturbation and simulation study SIAM J Appl Math 57 631-648
  • [2] Chen D P(2000)Long Time Behavior of Solutions to Nernst-Planck and Debye-Hückel Drift-Diffusion Systems Annales Henri Poincaré 1 461-472
  • [3] Eisenberg R S(1994)The Debye system: existence and large time behavior of solutions Nonlinear Anal 23 1189-1209
  • [4] Jerome J(2004)Diffuse-charge dynamics in electrochemical systems Physical review E 70 021,506-7663
  • [5] Biler P(1999)Ion channels gated by heat Proc Natl Acad Sci USA 96 7658-3009
  • [6] Dolbeault J(2013)Endpoint bilinear estimates and applications to the two-dimensional Poisson-Nernst-Planck system Nonlinearity 26 2993-25
  • [7] Biler P(2012)Optimal decay rates to conservation laws with diffusion-type terms of regularity-gain and regularity-loss Math Models Methods Appl Sci 22 1250012-24
  • [8] Hebisch W(1996)Computing the field in proteins and channels J Membrane Biol 150 1-1050
  • [9] Nadzieja T(1999)From structure to function in open ionic channels J Membrane Biol 171 1-1966
  • [10] Bazant M Z(2019)Finite domain effects in steady state solutions of Poisson-Nernst-Planck equations SIAM J Appl Math 79 1030-108
123456789