标题： 四阶聚集-扩散方程中的竞争效应 显示英文标题

标题： Competing effects in fourth-order aggregation-diffusion equations

摘要： 我们给出了关于带有向后二阶退化扩散的Cahn-Hilliard型方程的全局时间梯度流解的精确条件，在任何维度和一般初始数据下。 我们的方程是具有两种竞争效应的自由能的2-Wasserstein梯度流：Dirichlet能量和幂律内能。 泛函的齐次性揭示了我们需要分析的关键区域。 通过最小化运动方案，也称为JKO方案，构造的全局时间解的精确条件得到了。 此外，我们研究了一个具有类似梯度流结构的两个Cahn-Hilliard型方程的系统。 显示英文摘要

摘要： We give sharp conditions for global in time existence of gradient flow solutions to a Cahn-Hilliard-type equation, with backwards second order degenerate diffusion, in any dimension and for general initial data. Our equation is the 2-Wasserstein gradient flow of a free energy with two competing effects: the Dirichlet energy and the power-law internal energy. Homogeneity of the functionals reveals critical regimes that we analyse. Sharp conditions for global in time solutions, constructed via the minimising movement scheme, also known as JKO scheme, are obtained. Furthermore, we study a system of two Cahn-Hilliard-type equations exhibiting an analogous gradient flow structure.