一类带有时变系数的分数阶扩散方程解的爆破性  

Blow-Up of Solutions for a Class of Fractional Diffusion Equations with Time Dependent Coefficients

作　　者：高晓茹 李建军[1] 徒君[1] Gao Xiaoru;Li Jianjun;Tu Jun(College of science,Liaoning Technical University,Liaoning Fucin 123000)

机构地区：[1]辽宁工程技术大学理学院,辽宁阜新123000

出　　处：《数学物理学报（A辑）》2024年第5期1230-1241,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(51704140)。

摘　　要：该文主要研究了一类带有时间系数的分数阶扩散方程初边值问题解的爆破性.采用位势阱理论,Nehari流形,凹凸性等方法,结合各种微分不等式技巧,分别证明了次临界初始能级,负初始能级和任意正初始能级的情况下解的爆破性,并且给出了爆破时间的上界估计.特别地,由于能量泛函和位势阱深与时变系数f(t)有关,所以在次临界初始能级的情况下,爆破时间的上界会随着时变系数f(t)的变化而变化.In this paper,the blow-up properties of solutions for a class of fractional diffusion equations with time dependent coefficients is studied.By means of the potential well theory,Nehari manifold,concave conex method,and various differential inequalities,the finite time blow-up of the solutions under subcritical initial energy level,negative initial energy level and any positive initial energy level is discussed.And the upper bound of blow-up time is obtained.In particular,due to the energy functional and the depth of the potential well are related to the time-dependent coefficient f(t),in the case of sub-critical initial energy level,the upper bound of blow-up time will change with f(t).

关 键 词：分数阶 时变系数 位势阱 爆破 

分 类 号：O175.2[理学—数学]