• Corpus ID: 238744464

Existence of solutions to the Poisson--Nernst--Planck system with singular permanent charges in $\mathbb{R}^2$

@inproceedings{Hsieh2021ExistenceOS,
  title={Existence of solutions to the Poisson--Nernst--Planck system with singular permanent charges in \$\mathbb\{R\}^2\$},
  author={Chia Yu Hsieh and Yong Yu},
  year={2021}
}
  • C. Hsieh, Yong Yu
  • Published 13 October 2021
  • Mathematics
In this paper, we study the well-posedness of Poisson–Nernst–Planck system with no-flux boundary condition and singular permanent charges in two dimension. The main difficulty comes from the lack of integrability of singular permanent charges. In order to overcome the difficulty, the main idea is to transform the system into another weighted parabolic system. By choosing suitable weighted spaces, local existence of solutions can be obtained based on a fixed-point argument. Moreover, we also… 

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