Ahmad Fino, Grzegorz Karch
Published 2008-12-29Version 1
The large time behavior of nonnegative solutions to the reaction-diffusion equation $\partial_t u=-(-\Delta)^{\alpha/2}u - u^p,$ $(\alpha\in(0,2], p>1)$ posed on $\mathbb{R}^N$ and supplemented with an integrable initial condition is studied. We show that the anomalous diffusion term determines the large time asymptotics for $p>1+{\alpha}/{N},$ while nonlinear effects win if $p\leq1+{\alpha}/{N}.$
On the Asymptotic Analysis of Problems Involving Fractional Laplacian in Cylindrical Domains Tending to Infinity
Uniqueness of radial solutions for the fractional Laplacian
Uniqueness and Nondegeneracy of Ground States for $(-Δ)^s Q + Q - Q^{α+1} = 0$ in $\mathbb{R}$
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