We study the properties of interfaces in solutions of the Cauchy problem for the nonlinear degenerate parabolic equation ut = Δum - up in Rn 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) ∇um-1 + ∇Π ]|Γ(t) where Π is the solution of the degenerate elliptic equation div (u∇Π) + up = 0, Π = 0 on Γ(t). We give explicit formulas which represent the interface Γ(t) as a bijection from Γ(0). It is proved that the solution u and its interface Γ(t) are analytic functions of time t and that they preserve the initial regularity in the spatial variables.
@article{urn:eudml:doc:40911,
title = {Interfaces in solutions of diffusion-absorption equations.},
journal = {RACSAM},
volume = {96},
year = {2002},
pages = {129-134},
mrnumber = {MR1915676},
zbl = {1290.35146},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40911}
}
Shmarev, Sergei. Interfaces in solutions of diffusion-absorption equations.. RACSAM, Tome 96 (2002) pp. 129-134. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40911/