The uniqueness of bounded weak solutions to strongly coupled parabolicequations in a bounded domain with no-flux boundary conditions is shown. Theequations include cross-diffusion and drift terms and are coupledselfconsistently to the Poisson equation. The model class contains specialcases of the Maxwell-Stefan equations for gas mixtures, generalizedShigesada-Kawasaki-Teramoto equations for population dynamics, andvolume-filling models for ion transport. The uniqueness proof is based on acombination of the $H^{-1}$ technique and the entropy method of Gajewski.
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机译：显示了在无磁通边界条件的有界域中强耦合抛物方程的有界弱解的唯一性。这些方程包括交叉扩散项和漂移项，并且与泊松方程自洽耦合。该模型类包含气体混合物的麦克斯韦-斯特凡方程的特例，种群动态的广义Shigesada-Kawasaki-Teramoto方程以及离子迁移的体积填充模型的特例。唯一性证明基于$ H ^ {-1} $技术和Gajewski的熵方法的组合。
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