分数阶漂移-扩散模型解的Gevrey解析性和衰减率  

Gevrey analyticity and decay rates of solutions for the fractional drift-diffusion model

作　　者：罗永轲 赵继红 LUO Yong-ke;ZHAO Ji-hong(School of Mathematics and Information Science,Baoji University of 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）》2023年第1期1-7,18,共8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);陕西省自然科学基础研究计划一般项目-面上项目(2022JM-034);陕西省教育厅自然科学专项科研计划(21JK0479);宝鸡文理学院研究生科研创新项目(YJSCX22YB28)。

摘　　要：目的研究一类分数阶漂移-扩散模型整体解的Gevrey解析性和衰减率,该模型是半导体中经典模型Poisson-Nernst-Planck方程组的推广模型,数学形式上表现为分数阶非线性抛物型和椭圆型偏微分方程耦合而成的混合型方程组。方法利用多线性奇异积分算子理论和Fourier微局部分析技术进行研究。结果与结论证明了分数阶漂移-扩散模型在临界Fourier-Besov空间中的整体解是Gevrey解析的,并得到了此整体解的衰减率。Purposes—To study the Gevrey analyticity and decay rates of global solutions for a class of fractional drift-diffusion model.The model is a generalization of the classical Poisson-Nernst-Planck equation set in semiconductor devices,which mathematically exhibits the mixed equation system coupled with fractional nonlinear parabolic and elliptic partial differential equations.Methods—The multilinear singular integral theories and the Fourier microlocal analysis are used to prove main results.Results and Conclusions—It is proved that the global-in-time solutions of this model are Gevrey analytical in critical Fourier-Besov spaces,with decay rates of these global solutions obtained.

关 键 词：分数阶漂移-扩散模型 整体解 Gevrey解析性 衰减率 

分 类 号：O175.28[理学—数学]