A note on the uniqueness of weak solutions to a class of cross-diffusion systems

• DOI: 10.1007/s00028-017-0420-4
• Publication Date: 2017-11-30T12:14:10Z
• Authors: Xiuqing Chen; Ansgar Jüngel
• Keywords: Weak solution; Poisson's equation

The uniqueness of bounded weak solutions to strongly coupled parabolic equations in a domain with no-flux boundary conditions is shown. include cross-diffusion and drift terms are self-consistently the Poisson equation. model class contains special cases Maxwell–Stefan for gas mixtures, generalized Shigesada–Kawasaki–Teramoto population dynamics, volume-filling models ion transport. proof based on combination $$H^{-1}$$ technique entropy method Gajewski.