A quasilinear parabolic perturbation of the linear heat equation (Q649758)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A quasilinear parabolic perturbation of the linear heat equation |
scientific article; zbMATH DE number 5986514
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A quasilinear parabolic perturbation of the linear heat equation |
scientific article; zbMATH DE number 5986514 |
Statements
A quasilinear parabolic perturbation of the linear heat equation (English)
0 references
6 December 2011
0 references
The paper under review deals with a quasilinear perturbation, through the mean curvature flow operator, of the classical linear heat equation. The main result establishes a necessary and sufficient condition for the existence of a positive solution. Next, it is shown that the solution is unique and is symmetric around \(1/2\). The asymptotic behaviour of this solution is also studied. The final section analyzes the dynamics of solutions and proposes some open problems.
0 references
quasilinear heat equation
0 references
positive steady-states
0 references
dynamics
0 references
mean curvature flow operator
0 references
0 references
0 references
0 references
