带记忆项时间依赖非经典扩散方程的适定性

数学理论与应用 ›› 2021, Vol. 41 ›› Issue (1): 102-111.

带记忆项时间依赖非经典扩散方程的适定性

唐志飘张江卫* 刘迪

长沙理工大学数学与统计学院, 长沙, 410114

出版日期:2021-03-30 发布日期:2021-08-10
通讯作者: 张江卫；E−mail：zjwmath@163.com

Well-posedness of Time-dependent Nonclassical Diffusion Equation with Memory

Online:2021-03-30 Published:2021-08-10
Contact: Corresponding author:Zhang Jiangwei；E−mail：zjwmath@163.com
Supported by:
This work was supported by Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering (Changsha University of Science and Technology), and National Natural Science Foundation of China(Nos. 11101053, 71471020) and Postgraduate Scientific Research Innovation Project of Hunan Province(Nos. CX20200891).

摘要/Abstract

摘要： 本篇论文, 我们主要讨论了一类带随时间变化参数阻尼项的非经典扩散方程. 首先, 使用Faedo-Galerkin方法并结合分析技巧得到了整体弱解的存在性. 其次, 得到了弱解的唯一性及其对初值的连续依赖性, 其中非线性项f满足任意阶指数增长.

关键词: 非经典扩散方程 , 整体弱解 , 满足任意阶指数增 , Galerkin方法

Abstract:

In this paper, we mainly discuss an important class of nonclassical diffusion equation which the additional damping terms

vary over time. The existence of global weak solution is obtained by using the method of Faedo-Galerkin and analytical techniques. Meanwhile, we also prove the uniqueness of the solution and the continuous dependence on initial value, where the nonlinearity f satisfies arbitrary polynomial growth.

Key words: Nonclassical diffusion equation , Global weak solution , Arbitrary polynomial growth , Galerkin's method

唐志飘张江卫刘迪. 带记忆项时间依赖非经典扩散方程的适定性[J]. 数学理论与应用, 2021, 41(1): 102-111.