一类非线性退缩抛物方程的Cauchy问题

A Class of the Cauchy Problem for the Nonlinear Degenerate Parabolic Equation

讨论带吸收项的非线性双重退缩抛物方程ut =div(| um|p-2 um) -uq 具有初值u(x ,0 ) =μ∈L∞loc(RN)的Cauchy问题 .利用正则化方法 ,首先得到了正则化问题非负古典解的一致估计 ,最后在初值满足一定的增长条件下 ,证明了双重退缩抛物方程Cauchy问题弱解的存在性与不存在性 .

In this paper,we study the Cauchy problem with initial datum u(x,0)=μ∈L ∞ loc (R N) for the nonlinear doubly degenerate parabolic equation with asborption u t=div(|u m| p-2 u m)-u q .First,the uniform estimate of the nonnegative classical solution for the regularization problem are obtained.Finally,it is proved by method of regularization that the existence and nonexistence of weak solution of the Cauchy problem under the initial datum satisfy some growth condition.