Abstract
The uniqueness of bounded weak solutions to strongly coupled parabolic equations in a bounded domain with no-flux boundary conditions is shown. The equations include cross-diffusion and drift terms and are coupled self-consistently to the Poisson equation. The model class contains special cases of the Maxwell–Stefan equations for gas mixtures, generalized Shigesada–Kawasaki–Teramoto equations for population dynamics, and volume-filling models for ion transport. The uniqueness proof is based on a combination of the \(H^{-1}\) technique and the entropy method of Gajewski.
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The first author acknowledges support from the National Natural Science Foundation of China (NSFC), Grant 11471050, and from the China Scholarship Council (CSC), file no. 201706475001, who financed his stay in Vienna. The second author acknowledges partial support from the Austrian Science Fund (FWF), Grants P27352, P30000, F65, and W1245.
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Chen, X., Jüngel, A. A note on the uniqueness of weak solutions to a class of cross-diffusion systems. J. Evol. Equ. 18, 805–820 (2018). https://doi.org/10.1007/s00028-017-0420-4
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DOI: https://doi.org/10.1007/s00028-017-0420-4