一类带有变指数非局部项的反应扩散方程解的爆破行为  

Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents

作　　者：田娅 秦瑶 向晶 TIAN Ya;QIN Yao;XIANG Jing(School of Science,Chongqing University of Posts and Telecommunications,Chongqing 400065,P.R.China)

机构地区：[1]重庆邮电大学理学院,重庆400065

出　　处：《应用数学和力学》2022年第10期1177-1184,共8页Applied Mathematics and Mechanics

摘　　要：该文考虑了一类带有变指数非局部项的反应扩散方程的爆破问题.首先,由不动点原理,证明了问题解的局部存在性和唯一性.其次,利用上下解方法,给出在齐次Dirichlet边界条件下,问题的解在有限时间发生爆破的充分条件,即变指数大于零且初始值足够大,并对爆破时间的上下界进行了估计.The blow-up problems of the solutions are considered for reaction-diffusion equations with nonlocal sources and variable exponents.Firstly,the local existence and uniqueness of solutions to the problem were proved under the fixed-point theorem.Secondly,by means of the super-and sub-solution method,some sufficient conditions for the occurrence of finitetime blow-up were determined under the homogeneous Dirichlet boundary conditions,i.e.,the variable exponent is positive and the initial value is large enough.Moreover,the estimates of upper and lower bounds of the blow-up time were given.

关 键 词：非局部项 变指数 有限时间爆破 爆破时间上下界 

分 类 号：O357.41[理学—流体力学]