论文标题
通过PDE二元性来解释概率度量空间中的连续性方程系统
Interpreting systems of continuity equations in spaces of probability measures through PDE duality
论文作者
论文摘要
我们在概率测量空间中引入了单个或传输方程系统的偶性解决方案的概念，让人想起非线性抛物线方程的粘度解决方案概念。在适当的假设下，我们对双重性的解决方案的概念相当于梯度流解决方案，以防单个方程式具有此结构。相比之下，我们可以处理一个非线性非局部，是否扩散的系统，即没有任何变化结构的PDE系统。
We introduce a notion of duality solution for a single or a system of transport equations in spaces of probability measures reminiscent of the viscosity solution notion for nonlinear parabolic equations. Our notion of solution by duality is, under suitable assumptions, equivalent to gradient flow solutions in case the single/system of equations has this structure. In contrast, we can deal with a quite general system of nonlinear nonlocal, diffusive or not, system of PDEs without any variational structure.
