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