具L^p初值的拟线性退化抛物方程的熵解

The Entropy Solution of a Quasilinear Degenerate Parabolic Equation

拟线性退化抛物方程来自于反应扩散等许多物理问题,有着深刻的应用背景．本文利用Young测度的概念和Div- Curl引理证明了在0≤U0(x)∈L2(R)∩Lp(R)和f是真正非线性函数的条件下,存在一Lp熵解．

The Quasilinear degenerate parabolic equation {δtu＋δxf（u）=δxxA（u）-u^p,（x,t）∈R＋^2=R×（0,＋∞）,u（x,0）=u0（x）,x∈R comes from reaction diffusion etc physics problems, its applied background is very profound. The paper proves that there is a entropy solution provided that and f is a genuinely nonlinear function. Young measure and Div-Curl Lemma act as important roles in our proof.