一类变指数退化抛物方程的解

Solutions of a Kind of Degenerate Parabolic Equation with Variable Exponent

考虑如下的变指数退化抛物方程v_(t)=div(b(x,t)|▽v|^(p(x,t)-2▽v))+N∑i=1g^(i)(x,t)∂γ_(i)(v)/∂x_(i)解的适定性问题。利用抛物正则化方法证明了解的存在性。对检验函数适当选取,证明了解的唯一性。在边界∂Ω上,扩散系数b(x,t)=0,解的唯一性可以不依赖于边界条件。

The well-posedness problem of a kind of degenerate parabolic equation v_(t)=div(b(x,t)|▽v|^(p(x,t)-2▽v))+N∑i=1g^(i)(x,t)∂γ_(i)(v)/∂x_(i)were considered.By a parabolically regularized method,the existence of weak solutions was proved.By choosing a suitable test function,the uniqueness of weak solution was also proved.The diffusion coefficient b(x,t)=0 on∂Ω,the uniqueness theory could be established which was independent of the boundary value condition.