Uniqueness for the doubly degenerate volume-filling chemotaxis system

Establish uniqueness of global weak solutions for the degenerate volume-filling chemotaxis system with diffusion and chemotactic sensitivity satisfying D(0)=D(1)=h(0)=h(1)=0, under the setting considered by Bai, Kim, and Umezu.

Background

The paper surveys prior results on degenerate chemotaxis systems with volume-filling effects. For the case treated in [BKU-2007-MMMAS], both endpoint degeneracy of the diffusion, D(0)=D(1)=0, and vanishing of the chemotactic sensitivity at the endpoints, h(0)=h(1)=0, are imposed.

The cited work establishes existence and local Hölder continuity of global weak solutions, but does not establish their uniqueness. The present paper addresses uniqueness for a different source-term system under additional structural assumptions, so the unresolved uniqueness issue identified for the earlier doubly degenerate setting remains a distinct open problem.