论文标题
各向异性钢化扩散方程
Anisotropic tempered diffusion equations
论文作者
论文摘要
我们介绍了一个功能框架，该功能框架非常适合制定钢化体扩散类型的几类各向异性进化方程。在一组涉及非常自然电位功能的假设集合下，可以证明这些模型属于由4、5设计的熵解决方案框架，从而确保了适当的性能。我们将这种潜力的属性与相关成本函数的属性联系起来，从而提供了与最佳运输理论的联系，并提供了相对论成本函数的新示例。此外，我们表征了这些模型的各向异性扩散特性，并确定了兰金·休假的条件，这些条件是在给定各向异性流动下统治跳跃超浮面的时间演变。
We introduce a functional framework which is specially suited to formulate several classes of anisotropic evolution equations of tempered diffusion type. Under an amenable set of hypothesis involving a very natural potential function, these models can be shown to belong to the entropy solution framework devised by 4, 5, therefore ensuring well-posedness. We connect the properties of this potential with those of the associated cost function, thus providing a link with optimal transport theory and a supply of new examples of relativistic cost functions. Moreover, we characterize the anisotropic spreading properties of these models and we determine the Rankine-Hugoniot conditions that rule the temporal evolution of jump hypersurfaces under the given anisotropic flows.
