Proceedings of the Royal Society of Edinburgh **128A**(1998), 1281–1291

Original available at doi:S0308210500027323

Citations on Google Scholar

Original available at doi:S0308210500027323

Citations on Google Scholar

We prove that a class of weighted semilinear reaction diffusion equations on \(\mathbb R^N\) generates gradient-like semiflows on the Banach space of bounded uniformly continuous functions on \(\mathbb R^N\). If \(N = 1\) 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 semigroup.

**AMS Subject Classification (2000):**
47D06, 35B09, 35C10

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