一类发展的p(x)-Laplace方程解的存在唯一性  

Existence and Uniqueness of Solutions to an Evolutionary p(x)-Laplace Equation

作　　者：曾羽群[1] ZENG Yuqun(School of Science,Jimei University,Xiamen 361021,China)

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《集美大学学报（自然科学版）》2021年第2期119-124,共6页Journal of Jimei University：Natural Science

摘　　要：讨论一类发展的p(x)-Laplace方程ut=div(a(x,t)up(x)-2u)+f(u,x,t)解的存在唯一性。不同于此前的研究,文中假设a(x,t)≥0,且当x∈Ω时,a(x,t)>0,解的稳定性是建立在一个合理的部分边界条件u(x,t)=0,(x,t)∈Σ1上,其中Σ1■Ω×(0,T)仅仅是一个子流形。The following evolutionary p(x)-Laplace equations ut=div(a(x,t)up(x)-2u)+f(u,x,t)were discussed,and the existence and the uniqueness of weak solutions were proved.Different from the previous works,it was assumed a(x,t)≥0and a(x,t)x∈Ω>0 in this paper.The stability of weak solutions was based on a reasonable partial boundary value condition u(x,t)=0,(x,t)∈Σ1,whereΣ1■Ω×(0,T)was just a submanifold.

关 键 词：发展的p(x)-Laplace方程 存在唯一性 稳定性 部分边界条件 子流形 

分 类 号：O175.29[理学—数学]