55 citations · 69 across the 17 of their papers we have counts for
20 papers
Edmunds-Evans essential spectra of the generalized Constantin-Lax-Majda linearization
Jie Xu
For , we study the linearization about a smooth odd self-similar collapse profile of the generalized Constantin-Lax-Majda equation, where is the focusi…
The spectral picture of self-similar collapse in the Constantin-Lax-Majda equation
Jie Xu
We give a spectral description of the self-similar collapse profile of the Constantin-Lax-Majda (CLM) equation, the anchor of the generalized family $w_t + a\,u\,w_x = u_x\,w…
A second-order length-preserving and unconditionally energy stable rotational discrete gradient method for Oseen-Frank gradient flows
Jie Xu, Xiaotian Yang, Zhiguo Yang
We present a second-order strictly length-preserving and unconditionally energy-stable rotational discrete gradient (Rdg) scheme for the numerical approximation of the Oseen-Frank…
Prescribed Scalar Curvature Problem under Conformal Deformation of A Riemannian Metric with Dirichlet Boundary Condition
Jie Xu
In this article, we first show that for all compact Riemannian manifolds with non-empty smooth boundary and dimension at least 3, there exists a metric, pointwise conformal to the…
Prescribed Scalar Curvature on Compact Manifolds Under Conformal Deformation
Jie Xu
We give sufficient and "almost" necessary conditions for the prescribed scalar curvature problems within the conformal class of a Riemannian metric for both closed manifolds…
The Boundary Yamabe Problem, II: General Constant Mean Curvature Case
Jie Xu
This article uses the iterative schemes and perturbation methods to completely solve the Han-Li conjecture, i.e. the general boundary Yamabe problem with prescribed constant scalar…
The Boundary Yamabe Problem, I: Minimal Boundary Case
Jie Xu
We apply iteration schemes and perturbation methods to provide a complete solution of the boundary Yamabe problem with minimal boundary scenario, or equivalently, the existence of…
Solving the Yamabe-Type Equations on Closed Manifolds by Iteration Schemes
Jie Xu
We introduce a double iterative scheme and local variational method to solve the Yamabe-type equation …
Solving the Yamabe Problem by an Iterative Method on a Small Riemannian Domain
Steven Rosenberg, Jie Xu
We introduce an iterative scheme to solve the Yamabe equation on small domains equipped with a Riemannian metric . T…
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 . The nPBE is a model equation in nonline…
Newton's Method for M-Tensor Equations
Dong-Hui Li Jie-Feng Xu, Hong-Bo Guan
We are concerned with the tensor equations whose coefficient tensor is an M-tensor. We first propose a Newton method for solving the equation with a positive constant term and esta…
Solving Yamabe Problem by An Iterative Method
Jie Xu
We introduce an iterative scheme to prove the Yamabe problem , firstly on open domain with Dirichlet boundary conditions, and then on clos…
Inexact Newton Method for M-Tensor Equations
Dong-Hui Li, Hong-Bo Guan, Jie-Feng Xu
We first investigate properties of M-tensor equations. In particular, we show that if the constant term of the equation is nonnegative, then finding a nonnegative solution of the e…
Unconditionally positivity preserving and energy dissipative schemes for Poisson--Nernst--Planck equations
Jie Shen, Jie Xu
We develop a set of numerical schemes for the Poisson--Nernst--Planck equations. We prove that our schemes are mass conservative, uniquely solvable and keep positivity unconditiona…
Wave Approximation of Backward Heat Equation with Ricci Flow
Jie Xu
In this paper, we consider solutions of the backward heat equation with Ricci flow on manifolds as a type of infinite dimensional limit of solutions of a wave equation on a larger…
Central Limit Theorems on Compact Metric Spaces
Steven Rosenberg, Jie Xu
We produce a series of Central Limit Theorems (CLTs) associated to compact metric measure spaces , with a reasonable probability measure. For the first CLT, we can ign…
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 with Dirichlet or Neumann boundar…
Averages of Unlabeled Networks: Geometric Characterization and Asymptotic Behavior
Eric Kolaczyk, Lizhen Lin, Steven Rosenberg +2
It is becoming increasingly common to see large collections of network data objects -- that is, data sets in which a network is viewed as a fundamental unit of observation. As a re…
Basic Properties of Singular Fractional Order System with order (1,2)
Xiaogang Zhu, Jie Xu, Junguo Lu
This paper focuses on some properties, which include regularity, impulse, stability, admissibility and robust admissibility, of singular fractional order system (SFOS) with fractio…
A stochastic collocation approach for parabolic PDEs with random domain deformations
Julio E. Castrillon-Candas, Jie Xu
This work considers the problem of numerically approximating statistical moments of a Quantity of Interest (QoI) that depends on the solution of a linear parabolic partial differen…