SMS scnews item created by Daniel Daners at Fri 30 Sep 2011 1537
Type: Seminar
Modified: Fri 30 Sep 2011 1903
Distribution: World
Expiry: 5 Oct 2011
Calendar1: 5 Oct 2011 1400-1500
CalLoc1: AGR Carslaw 829
Auth: daners@d220-237-34-126.mas801.nsw.optusnet.com.au (ddan2237) in SMS-WASM

# Front propagation in nonlinear diffusion equations on hyperbolic space

### Matano

Hiroshi Matano
The University of Tokyo, Japan
5th October 2011, 2-3pm, Carslaw 829 (Access Grid Room)

## Abstract

In this talk I will discuss the front propagation for a certain class of nonlinear diffusion equations on hyperbolic space $$\mathbb H^n$$. More specifically we consider solutions whose intital data are nonnegative and compactly supported, and study how their fronts (i.e. the level surfaces near the transition layer) spread over the space. Much attention will be directed to the similarities as well as the differences between the case of $$\mathbb H^n$$ and that of the Euclidean space $$\mathbb R^n$$.

Among other things we show that the global shape of the expanding fronts will remain close to an expanding geodesic sphere, while the local profile of the solution near the front area converges to what we call a "horospheric wave".

This is joint work with Fabio Punzo and Alberto Tesei.

Check also the PDE Seminar page. Enquiries to Florica Cîrstea or Daniel Daners.

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