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This fixed point is a weak solution of the coupled system 3. Multiplying the NP equation 1. From 1.

Similar to 1. Then the NP equation 1.

In other words, we proved the uniformly Lipschitz continuity of mapping T. Therefore, we proved the existence of weak solution to the system 3. Rights and permissions About this article Cite this article Hu, J.

A fully discrete positivity-preserving and energy-dissipative finite difference scheme for Poisson—Nernst—Planck equations.