Gradient-like parabolic semiflows on BUC(ℝN)
Daniel Daners, Sandro Merino · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1998
We prove that a class of weighted semilinear reaction diffusion equations onRNgenerates gradient-like semiflows on the Banach space of bounded uniformly continuous functions onRN. IfN= 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.