Strong Competition versus Fractional Diffusion: The Case of Lotka-Volterra Interaction
Strong Competition versus Fractional Diffusion: The Case of Lotka-Volterra Interaction
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DOI：
10.1080/03605302.2014.890627
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发表时间：
2013-10
影响因子：
1.9
通讯作者：
G. Verzini;A. Zilio
中科院分区：
文献类型：
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作者：
G. Verzini;A. Zilio
考虑一类具有非线性Steklov边界条件的微分方程组，它与分数阶问题有关，其中u =（u1，...，uk），s ∈（0，1），p > 0，aij> 0，β > 0.当k = 2时，我们发展了一个关于α0，α，一致w.r.t.的拟最优正则性理论。当α < αopt = min（1，2s）时，极限轮廓的迹线是Lipschitz连续的，并且是分离的.在对s，p和aij作了某些限制的情况下，将这些结果推广到k ≥ 3密度的情形.由于竞争的变分型的最佳规律性是已知的，这些结果标志着一个实质性的差异与标准扩散s = 1的情况下，其中两个竞争不能区分彼此的限制。
We consider a system of differential equations with nonlinear Steklov boundary conditions, related to the fractional problem where u = (u 1,…, u k ), s ∈ (0, 1), p > 0, a ij > 0 and β > 0. When k = 2 we develop a quasi-optimal regularity theory in 𝒞0, α, uniformly w.r.t. β, for every α < αopt = min (1, 2s); moreover we show that the traces of the limiting profiles as β → + ∞ are Lipschitz continuous and segregated. Such results are extended to the case of k ≥ 3 densities, with some restrictions on s, p and a ij . Since for competition of variational type the optimal regularity is known to be , these results mark a substantial difference with the case of standard diffusion s = 1, where the two competitions cannot be distinguished from each other in the limit.