𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Nonlinear Diffusion Equations on Unbounded Fractal Domains

✍ Scribed by Kenneth J. Falconer; Jiaxin Hu

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
144 KB
Volume
256
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

We investigate the nonlinear diffusion equation βˆ‚u/βˆ‚t = u + u p p > 1 on certain unbounded fractal domains, where is the infinitesimal generator of the semigroup associated with a corresponding heat kernel. We show that there are nonnegative global solutions for non-negative initial data if p > 1 + 2/d s , while solutions blow up if p ≀ 1 + 2/d s , where d s is the spectral dimension of the domain. We investigate smoothness and HΓΆlder continuity of solutions when they exist.

πŸ“œ SIMILAR VOLUMES

On nonlinear diffusion equations
On nonlinear diffusion equations
✍ Barry M. Cherkas πŸ“‚ Article πŸ“… 1972 πŸ› Elsevier Science 🌐 English βš– 580 KB
On nonlinear diffusion equations
On nonlinear diffusion equations
✍ C.T Taam πŸ“‚ Article πŸ“… 1967 πŸ› Elsevier Science 🌐 English βš– 826 KB
The Generalized Quasi-linearization Meth
The Generalized Quasi-linearization Method for Reaction Diffusion Equations on an Unbounded Domain
✍ A.S. Vatsala; Liwen Wang πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 92 KB

The method of generalized quasi-linearization has been well developed for ordinary differential equations. In this paper, we extend the method of generalized quasi-linearization to reaction diffusion equations on an unbounded domain. The iterates, which are solutions of linear equations starting fro

Infinite-dimensional exponential attract
Infinite-dimensional exponential attractors for fourth-order nonlinear parabolic equations in unbounded domains
✍ Messoud Efendiev πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 189 KB

## Communicated by W. Sprâßig We study in this article the long-time behavior of solutions of fourth-order parabolic equations in R 3 . In particular, we prove that under appropriate assumptions on the nonlinear interaction function and on the external forces, these equations possess infinite-dime