Interfaces in solutions of diffusion-absorption equations.
We study the properties of interfaces in solutions of the Cauchy problem for the nonlinear degenerate parabolic equation u = Δu - u in R x (0,T] with the parameters m > 1, p > 0 satisfying the condition m + p ≥ 2. We show that the velocity of the interface Γ(t) = ∂{supp u(x,t)} is given by the formula v = [ -m / (m-1) ∇u + ∇Π ]| where Π is the solution of the degenerate elliptic equation div (u∇Π) + u = 0, Π = 0 on Γ(t). We give explicit formulas which represent the interface Γ(t)...