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Existence of solutions to the Poisson--Nernst--Planck system with singular permanent charges in
Chia-Yu Hsieh, Yong Yu
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 come…
Long-time dynamics of classical Patlak-Keller-Segel equation
Chia-Yu Hsieh, Yong Yu
When the spatial dimension , it has been well-known that a global mild solution to classical Patlak-Keller-Segel equation (PKS equation for short) exists if and only if its i…
Global Existence of the Non-isothermal Poisson-Nernst-Planck-Fourier System
Chia-Yu Hsieh, Tai-Chia Lin, Chun Liu +1
In this paper, we consider a non-isothermal electrokinetic model, which is derived from the Energetic Variational Approach. The charge transport is described through the Poisson-Ne…
Exponential decay estimates for the stability of boundary layer solutions to Poisson-Nernst-Planck systems: one spatial dimension case
Chia-Yu Hsieh, Tai-Chia Lin
With a small parameter , Poisson-Nernst-Planck (PNP) systems over a finite one-dimensional (1D) spatial domain have steady state solutions, called 1D boundary layer solutions, w…