带记忆项时间依赖非经典扩散方程的适定性  

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

作　　者：唐志飘 张江卫 刘迪 Tang Zhipiao;Zhang Jiangwei;Liu Di(School of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410114,China)

机构地区：[1]长沙理工大学数学与统计学院,长沙410114

出　　处：《数学理论与应用》2021年第1期102-111,共10页Mathematical Theory and Applications

基　　金：supported by Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering (Changsha University of Science and Technology);National Natural Science Foundation of China (Nos. 11101053, 71471020);Postgraduate Scientific Research Innovation Project of Hunan Province (No. CX20200891)。

摘　　要：本文讨论一类带随时间变化参数阻尼项的非经典扩散方程.首先,使用非经典Faedo-Galerkin方法并结合分析技巧得到整体弱解的存在性.其次,得到弱解的唯一性及其对初值的连续依赖性,其中非线性项f满足任意阶多项式增长.In this paper, we discuss a class of nonclassical diffusion equation with time-dependent damping terms.The existence of global weak solution is obtained by using the nonclassical 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.

关 键 词：非经典扩散方程 整体弱解 任意阶多项式增长 GALERKIN方法 

分 类 号：O175.2[理学—数学]