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Decay of mass for nonlinear equation with fractional Laplacian |
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| Authors: | Ahmad Fino Grzegorz Karch |
| Institution: | 1. Laboratoire MIA et Département de Mathématiques, Université de La Rochelle, Avenue Michel Crépeau, 17042, La Rochelle Cedex, France 2. LaMA-Liban, Lebanese University, P. O. Box 826, Tripoli, Lebanon 3. Instytut Matematyczny, Uniwersytet Wroc?awski, pl. Grunwaldzki 2/4, 50-384, Wroc?aw, Poland |
| Abstract: | The large time behavior of non-negative 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 + α/N, while nonlinear effects win if p ≤ 1 + α/N. |
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