# Interfaces in solutions of diffusion-absorption equations.

RACSAM (2002)

- Volume: 96, Issue: 1, page 129-134
- ISSN: 1578-7303

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topShmarev, 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 > 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.},

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 > 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.

LA - eng

KW - Ecuaciones parabólicas; Problema de Cauchy; Ecuaciones de evolución; Proceso de difusión

UR - http://eudml.org/doc/40911

ER -