Interfaces in solutions of diffusion-absorption equations.

Shmarev, Sergei. "Interfaces in solutions of diffusion-absorption equations.." RACSAM 96.1 (2002): 129-134. <http://eudml.org/doc/40911>.

@article{Shmarev2002,
abstract = {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 &gt; 1, p &gt; 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.},
author = {Shmarev, Sergei},
journal = {RACSAM},
keywords = {Ecuaciones parabólicas; Problema de Cauchy; Ecuaciones de evolución; Proceso de difusión},
language = {eng},
number = {1},
pages = {129-134},
title = {Interfaces in solutions of diffusion-absorption equations.},
url = {http://eudml.org/doc/40911},
volume = {96},
year = {2002},
}

TY - JOUR
AU - Shmarev, Sergei
TI - Interfaces in solutions of diffusion-absorption equations.
JO - RACSAM
PY - 2002
VL - 96
IS - 1
SP - 129
EP - 134
AB - 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 &gt; 1, p &gt; 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.
LA - eng
KW - Ecuaciones parabólicas; Problema de Cauchy; Ecuaciones de evolución; Proceso de difusión
UR - http://eudml.org/doc/40911
ER -