Jie Xu

activity

20142026

most citedUnconditionally positivity preserving and energy dissipative schemes for Poisson--Nernst--Planck equations

55 citations · 69 across the 17 of their papers we have counts for

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math.AP2026

Edmunds-Evans essential spectra of the generalized Constantin-Lax-Majda linearization

Jie Xu

For $0 < a < 1$ , we study the linearization $L_{a}$ about a smooth odd self-similar collapse profile $(Ω, c_{l})$ of the generalized Constantin-Lax-Majda equation, where $c_{l}$ is the focusi…

math.AP2021

Existence of Strong Solution for the Complexified Non-linear Poisson Boltzmann Equation

Brian Choi, Jie Xu, Trevor Norton +2

We prove the existence and uniqueness of the complexified Nonlinear Poisson-Boltzmann Equation (nPBE) in a bounded domain in $R^{3}$ . The nPBE is a model equation in nonline…

math.AP2020

Solving Yamabe Problem by An Iterative Method

Jie Xu

We introduce an iterative scheme to prove the Yamabe problem $- a Δ_{g} u + S u = λ u^{p - 1}$ , firstly on open domain $(Ω, g)$ with Dirichlet boundary conditions, and then on clos…

math.AP2019

Iterative Methods for Globally Lipschitz Nonlinear Laplace Equations

Jie Xu

We introduce an iterative method to prove the existence and uniqueness of the complex-valued nonlinear elliptic PDE of the form $- Δ u + F (u) = f$ with Dirichlet or Neumann boundar…