一类发展的p(x)-Laplace方程解的存在唯一性

讨论一类发展的p(x)-Laplace方程ut=div(a(x,t)|▽u|p(x)-2▽u)+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...

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

The following evolutionary p(x)-Laplace equations t=div(a(x,t)∣△u∣p(x)－2△u)+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,where Σ1Ω×(0,T) was just a submanifold.