# Gradient-like Parabolic Semiflows on BUC(R^N)

## Author

**Daniel Daners** and **Sandro Merino**

## Status

Research Report 97-20

Date: 6 June 1997

## Abstract

We prove that a class of weighted semilinear reaction diffusion
equations on R^N generates gradient-like semiflows on the Banach space
of bounded uniformly continuous functions on R^N. In one dimension we
show convergence to a single equilibrium. The key for getting the
result is to show the exponential decay of the stationary solutions,
which is obtained by means of a decay estimate of the kernel of the
underlying linear semigroup.

## Key phrases

semilinear parabolic equations. omega limit sets. attractors.

## AMS Subject Classification (1991)

Primary: 35B40

Secondary: 35K15

## Content

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Sydney Mathematics and Statistics