PROPERTIES OF THE BOUNDARY FLUX OF A SINGULAR DIFFUSION PROCESS

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The authors study the singular diffusion equation(6)u/(6)t = div(pα|(△)u|p-2(△)u), (x,t) ∈ QT = Ω× (0,T),where Ω (C) Rn is a bounded domain with appropriately smooth boundary (6)Ω, p(x) =dist(x, (6)Ω), and prove that if α≥ p- 1, the equation admits a unique solution subject only to a given initial datum without any boundary value condition, while if 0 <α<p- 1, for a given initial datum, the equation admits different solutions for different boundary value conditions.
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