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.
semilinear parabolic equations. omega limit sets. attractors.
AMS Subject Classification (1991)
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Sydney Mathematics and Statistics