摘要
考虑具有变指数的退化抛物方程u t=div(ραa(u)p(x)-2 a(u))+g(x)div(b(u))弱解的存在唯一性问题,其中ρ(x)=dist(x,∂Ω)是其到边界的距离函数,a(s)是一个严格单调上升的函数.通过选取合适的检验函数证明在无边界值条件情形下该方程弱解的唯一性成立.
The existence and the uniqueness of weak solutions to a degenerate parabolic equation with variable exponents u t=div(ραa(u)p(x)-2 a(u))+g(x)div(b(u))is considered,whereρ(x)=dist(x,∂Ω)is the distance function from the boundary,a(s)is a strictly monotone increasing function.By choosing a sui table test function,the uniqueness of weak solution of the equation is proved under the condition of no boundary value.
作者
詹华税
袁洪君
ZHAN Huashui;YUAN Hongjun(School of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,Fujian Province,China;College of Mathematics,Jilin University,Changchun 130012,China)
出处
《吉林大学学报(理学版)》
CAS
北大核心
2021年第1期1-6,共6页
Journal of Jilin University:Science Edition
基金
福建省自然科学基金(批准号:2019J01858).
关键词
退化抛物方程
变指数
边界值条件
稳定性
唯一性
degenerate parabolic equation
variable exponent
boundary value condition
stability
uniqueness