时间加权非局部反应扩散方程解的性质  

The Properties of Solutions for the Nonlocal Diffusion Equation with Time-weighted Coefficients

作　　者：余巧云 孟海霞[1] YU Qiaoyun;MENG Haixia(School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《佳木斯大学学报（自然科学版）》2021年第1期145-148,共4页Journal of Jiamusi University：Natural Science Edition

基　　金：国家自然科学基金地区基金项目(11961039);甘肃省自然科学基金(1310RJZA070)。

摘　　要：研究了带有Dirichlet边界条件和具有时间加权系数非局部源项的非局部扩散方程解的存在性与爆破性.首先,在非负非平凡有界初值条件下,运用Banach不动点理论得到了解的存在性与唯一性.其次,利用时间加权系数及其特征函数构造了一个新的指数型辅助函数.最后,运用微分理论,结合Schwarz及其Holder等一系列不等式,得到了解在有限时刻内爆破的充分条件及其解的爆破时间的上界估计.The paper studied the local existence and blowup of solutionsfor the diffusion equationwith Dirichlet boundary conditions and nonlocal source term with time-weighted coefficients.Firstly,under the conditions of nonnegative nontrivial bounded initial value,using the Banach fixed point theory,the existence and uniqueness of solutions was obtained.Secondly,a new exponential auxiliary function was constructed by using the time-weighted coefficients and eigenfunctions.Finally,by using the differential theory,and combining with a series of inequalities such as Schwarz and Holder,the sufficient conditions for blowup and the upper bounds estimation of blowup time were derived.

关 键 词：非局部扩散 时间加权系数 非局部反应源 存在性 爆破性 

分 类 号：O175.26[理学—基础数学]