热防护服中反常热扩散方程Robin问题的条件适定性  

Conditional well-posedness of Robin problem for anomalous thermal diffusion equations of thermal protective clothing

作　　者：彭鹏 徐定华[1] PENG Peng;XU Dinghua(School of Sciences,Zhejiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]浙江理工大学理学院,杭州310018

出　　处：《浙江理工大学学报（自然科学版）》2020年第2期267-271,共5页Journal of Zhejiang Sci-Tech University(Natural Sciences)

基　　金：国家自然科学基金项目(11871435,11471287)。

摘　　要：根据连续时间随机游走理论,建立热防护服中具有反常热扩散规律和分数阶Robin边界条件的空间分数阶模型,用以描述高温环境下各向同性材料内部及边界上的热传递规律。针对该模型,首先提出了该模型的变分形式,并通过乘以一个简单函数因子,消除了此模型齐次问题的奇异性,给出了变分问题弱解的定义;然后根据分数阶导数算子和分数阶积分算子的性质证明了该模型的条件适定性,即弱解的能量估计和弱解的唯一性。反常扩散方程Robin问题的条件适定性结果有利于分析数值算法的收敛性,并为热防护服性能评估提供理论指导。According to the theory of continuous time random walk,a spatial fractional order model with anomalous thermal diffusion law and fractional Robin boundary condition was established to describe the heat transfer law inside and on the boundary of isotropic materials under high temperature environment.Aiming at the model,the variational form of the model was first presented.The singularity of the homogeneous problem of this model was eliminated by multiplying a simple function factor,and the definition of the weak solution of the variational problem was further given.Then,based on the properties of the fractional derivative operator and the fractional integral operator,we proved the conditional well-posedness of the model,that is,the energy estimation of the weak solution and the uniqueness of the weak solution.The conditional well-posedness results of anomalous diffusion equations contribute to analyzing the convergence of numerical algorithm and provide theoretical guidance for performance evaluation of thermal protective clothing.

关 键 词：反常热扩散 分数阶Robin边界条件 空间分数阶模型 变分形式 弱解 

分 类 号：O242-1[理学—计算数学]