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 Andreu et al. (2005), 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.

我们介绍一个功能框架，该框架特别适合于拟定几类回火扩散类型的各向异性演化方程。在一个涉及一个非常自然的势函数的假设的前提下，这些模型可以证明属于Andreu等人设计的熵解框架。（2005年），因此确保适当的定位。我们将这种潜力的属性与相关的成本函数联系起来，从而提供了与最优运输理论的联系，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，并确定了在给定的各向异性流下支配跳跃超表面时间演变的兰金-休格尼特条件。