Publication: Gradient-like parabolic semiflows on BUC(ℝ$^{N}$)
Gradient-like parabolic semiflows on BUC(ℝ$^{N}$)
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Daners, D., & Merino, S. (1998). Gradient-like parabolic semiflows on BUC(ℝ$^{N}$). Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 128(6), 1281–1291. https://doi.org/10.1017/s0308210500027323
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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$^{N}$. 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.
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- Daners, Daniel
- Merino, Sandro
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Daners, D., & Merino, S. (1998). Gradient-like parabolic semiflows on BUC(ℝ$^{N}$). Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 128(6), 1281–1291. https://doi.org/10.1017/s0308210500027323
