On a Singular Diffusion Equation in Nondivergence Form

This paper studies a singular diffusion equation in nondivergence form with the Dirichlet boundary value and initial value Here p > 1,Ω(?) RN is a bounded domain with appropriately smooth boundary (?)Ω, and φ(u) satisfies the following condition (1.1) aries some models describing physical phenomenon. For example, if φ(u) = uq with q ∈[0,1), then (1.1) can be written in divergence form after the change of variables

This paper studies a singular diffusion equation in nondivergence form μ/ t = Ф（u）div（｜ u｜^P-2 u） in Q= Ω×（0,∞）, with the Dirichlet boundary value and initial value u（x,t）=0 on Ω×（0,∞）, u（x,0）=u0（x） in Ω.