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


Daniel Daners and Sandro Merino


Research Report 97-20
Date: 6 June 1997


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


The paper is available in the following forms:
TeX dvi format:
1997-20.dvi.gz (20kB) or 1997-20.dvi (46kB)

PostScript: (54kB) or (185kB)

To minimize network load, please choose the smaller gzipped .gz form if and only if your browser client supports it.

Sydney Mathematics and Statistics