Decay of mass for nonlinear equation with fractional Laplacian

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Fino, Ahmad
Karch, Grzegorz
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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 $p\leq1+{\alpha}/{N}.$
Keywords
Mathematics - Analysis of PDEs, 35K55, 35B40, 60H99
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