Research Interests:

  • Mathematical modeling of fluid systems and electrophysiology

  • Fast algorithms for partial differential equations and integral equations

  • Integral equation theory and classical density functional theory in complex fluids

  • Kinetic theory and its application in fluid dynamics

Publications:

  1. C.-Y. Hsieh, T.-C. Lin, C. Liu, P. Liu, Global Existence of the Non-isothermal Poisson-Nernst-Planck-Fourier System. Submitted (2020).

  2. J. Liang, P. Liu, Z. Xu, A fast Poisson solver of arbitrary order accuracy through the harmonic surface mapping algorithm. Submitted (2020).

  3. Y. Wang, C. Liu, P. Liu, B. Eisenberg, Field theory of reaction-diffusion: Mass action with an energetic variational approach . Submitted (2020).

  4. P. Liu, S. Wu and C. Liu, Non-Isothermal Electrokinetics: Energetic Variational Approach. Comm. Math. Sci., 5 (2018), pp. 1451–1463.

  5. Q. Zhao , P. Liu and Z. Xu, A fast method for evaluating Green's function in irregular domains with application to charge interaction in a nanopore. Commun. Comput. Phys., 24 (2018), pp. 1241-1258.

  6. L. Ji, P. Liu, Z. Xu and S. Zhou, Asymptotic Analysis on Dielectric Boundary Effects of Modified Poisson--Nernst--Planck Equations . SIAM J. Appl. Math., 78(3): 1802--1822, 2018.

  7. Z. Wu, P. Liu, Y. Liu, W. Wei, X. Zhang, P. Wang, Z. Xu and H. Xiong, Regulating sequence distribution of polyethers via ab initio kinetics control in anionic copolymerization. Polym. Chem.,8: 5673--5678, 2017.

  8. P. Liu, X. Ji and Z. Xu, Modified Poisson-Nernst-Planck model with accurate Coulomb correlation in variable media. SIAM J. Appl. Math., 78(1), 226--245, 2017.

  9. P. Liu, C. Liu and Z. Xu, Generalized Shockley-Ramo Theorem in electrolytes . Comm. Math. Sci., 15(2): 555--564, 2017.

  10. P. Liu, M. Ma and Z. Xu, Understanding depletion induced like-charge attraction from self-consistent field model. Comm. Comp. Phys., 22(1): 95--111, 2017.

  11. Z. Xu, M. Ma and P. Liu, Self-energy modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches. Phys. Rev. E., 90(1), 013307, 2014.

  12. B. Li, P. Liu, S. Zhou and Z. Xu, Ionic size effects: Generalized Boltzmann distributions, counterion stratification, and modified Debye length. Nonlinearity, 26(10): 2899--2922, 2013. Selected in the journal's Highlights of 2013.