论文标题
带有Riesz电位的非线性聚合扩散方程
Nonlinear aggregation-diffusion equations with Riesz potentials
论文作者
论文摘要
我们考虑了一个聚合扩散模型，其中扩散是多孔培养基类型的非线性，并且聚集受阶s的riesz的影响。二次扩散项的添加会产生更精确的竞争，而小s的聚合项则具有相同的比例，如果s = 0。我们证明了固定状态的存在和独特性，我们将其渐近行为表征为零。此外，我们通过应用JKO方案证明了梯度流解决方案的存在。
We consider an aggregation-diffusion model, where the diffusion is nonlinear of porous medium type and the aggregation is governed by the Riesz potential of order s. The addition of a quadratic diffusion term produces a more precise competition with the aggregation term for small s, as they have the same scaling if s=0. We prove existence and uniqueness of stationary states and we characterize their asymptotic behavior as s goes to zero. Moreover, we prove existence of gradient flow solutions to the evolution problem by applying the JKO scheme.
