Self-Similar Solutions of a Fast Diffusion Equation That Do Not Conserve Mass
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Self-Similar Solutions of a Fast Diffusion Equation That Do Not Conserve Mass
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| Id. |
41575567 |
| Idioma |
inglés
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| Titulo |
Self-Similar Solutions of a Fast Diffusion Equation That Do Not Conserve Mass |
| Autor(es) |
Mark A. Peletier,Hongfei Zhang
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| Localización |
http://citeseer.ist.psu.edu/141470.html
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| Versión |
1.0 |
| Estado |
Final
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| Descripción |
We consider self-similar solutions of the fast diffusion equation u t = r Delta (u
Gamman
ru)
in (0; 1) Theta R
N
, for N 3 and
2
N
! n ! 1, of the form
u(x; t) = (T Gamma t)
ff
f
Gamma
jxj (T Gamma t)
Gammafi
Delta
:
Because mass conservation does not hold for these values of n, this results in a
nonlinear eigenvalue problem for f and ff. We employ phase plane techniques to
prove existence and uniqueness of solutions (f; ff), and we investigate their behaviour
when n " 1 and when n#
2
N
.
1 Introduction
The equation
u t = r Delta (u
Gamman
ru) (1.1)
arises in many areas of applications. The case n = 0 corresponds to the classical heat conduction
equation. When n ! 0, the equation models the flow of a gas in a porous medium.
Because the diffusion coefficient u
Gamman
vanishes when u = 0, disturbances of u = 0 propagate
at finite speed. Therefore (1.1) with n ! 0 is also known as the slow diffusion equation,
and has been the focus of extensive study...
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| Tipo |
ps
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| Palabras clave |
Mark A. Peletier,Hongfei Zhang Self-Similar Solutions of a Fast Diffusion Equation That Do Not Conserve Mass
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| Tipo de Interactividad |
Expositivo
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| Nivel de Interactividad |
muy bajo
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| Audiencia |
Estudiante
Profesor
Autor
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| Estructura |
Atomic |
| Coste |
no
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| Copyright |
sí
|
|
unrestricted |
| Formatos |
ps
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| Requerimientos técnicos |
Browser: Any
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| Relación |
[IsBasedOn] ftp://ftp.twi.tudelft.nl/TWI/publications/tech-reports/1994/DUT-TWI-94-40.ps.gz
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| Fecha de contribución |
31-mar-2009 |
| Contacto |
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