具有变指数的退化抛物方程解的唯一性

Uniqueness of Solutions to Degenerate ParabolicEquation with Variable Exponents

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.