On some non linear evolution systems which are perturbations of Wasserstein gradient flows

Understand

This paper presents existence and uniqueness results for a class of parabolic systems with non linear diffusion and nonlocal interaction.

• These systems can be viewed as regular perturbations of Wasserstein gradient flows.
• Here we extend results known in the periodic case to the whole space and on a smooth bounded domain.
• Existence is obtained using a semi-implicit Jordan-Kinderlehrer-Otto scheme and uniqueness follows from a displacement convexity argument.