Poisson-Nernst-Planck方程组大解的整体存在性的一个新证明方法  

A new proof of global existence of large solutions for the Poisson-Nernst-Planck equations

作　　者：陈浩 靳荣 赵继红 CHEN Hao;JIN Rong;ZHAO Ji-hong(School of Mathematics and Information Science,Baoji University Arts and Sciences,Baoji 721013,Shaanxi,China)

机构地区：[1]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《宝鸡文理学院学报（自然科学版）》2024年第3期1-4,共4页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：国家自然科学基金项目(11961030);陕西省自然科学基金项目(2022JM-034)。

摘　　要：目的研究来源于半导体理论中刻画带电粒子漂移和扩散现象的Poisson-Nernst-Planck方程组,建立该方程组大解的整体存在性。方法利用加权法、扰动法和反证法进行研究。结果通过引入新的权函数建立了扰动方程在Chemin-Lerner混合时空空间中的非线性估计,然后利用反证法建立了Poisson-Nernst-Planck方程组大解的整体存在性。结论2类带电粒子密度函数之差在适定性理论中起着更重要的作用。Purposes—To study the Poisson-Nernst-Planck equations arising from the semiconductor theory,which describes the drift and diffusion phenomena of the charged particles,and to establish the global existence of large solutions to this equations.Methods—Weighted method,perturbation method and contradiction method were used.Results—By introducing a new weighted function,we establish the nonlinear estimates of the perturbed equations in the Chemin-Lerner mixed time-space spaces and obtain the global existence of large solutions to the Poisson-Nernst-Planck equations by contradiction method.Conclusion—The difference of two classes of charged particles plays more important role in the well-posed theory of this equations.

关 键 词：Poisson-Nernst-Planck方程组 大解 整体存在性 BESOV空间 

分 类 号：O175.29[理学—数学]