The Remormalized Entropy Solutions Of Quasilinear Anisotropic Degenerate Parabolic Equations With Time-Space Dependent Diffusion Coefficients

We define the renormlized entropy solutions of quasilinear anisotropic degenerate parabolic equations with explicit (t,x)-dependence:where a(u, t, x) = (a_ij(u, t,x)) = σ(u, t, x)σ(u, t, x)^T is nonnegtive definit.we establish the existence and uniqueness theory of the Cauchy problemAt last,establish a continuous dependence estimate for the spatial diffusion.