Porous medium equation and fast diffusion equation as gradient systems

Title:

Porous medium equation and fast diffusion equation as gradient systems

Creator:

Littig, Samuel and Voigt, Jürgen

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:3b312295-b060-4cc4-8d61-b41cb160bb93
uuid:3b312295-b060-4cc4-8d61-b41cb160bb93
issn:0011-4642

Subject:

mathematics, porous medium equation, gradient system, fast diffusion, asymptotic behaviour, order preservation, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

We show that the Porous Medium Equation and the Fast Diffusion Equation, \dot u - \Delta {u^m} = f with m\in (0, \infty ), can be modeled as a gradient system in the Hilbert space H^{-1}(\Omega ), and we obtain existence and uniqueness of solutions in this framework. We deal with bounded and certain unbounded open sets \Omega \subset \mathbb{R}^{n} and do not require any boundary regularity. Moreover, the approach is used to discuss the asymptotic behaviour and order preservation of solutions., Samuel Littig, Jürgen Voigt., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

869-889

Source:

Czechoslovak Mathematical Journal | 2015 Volume:65 | Number:4

Harvested from:

CDK

Metadata only:

false