54 citations · 110 across the 20 of their papers we have counts for
23 papers
Stochastic Homogenization of Non-local Hamilton-Jacobi-Bellman equations
Wenjia Jing, Qi Zhang
In this paper we apply the method of Kosygina, Rezakhanlou and Varadhan (CPAM 2006) to establish stochastic homogenization of Hamilton-Jacobi-Bellman (HJB) equation with a vanishin…
On the periodic homogenization of elliptic equations in non-divergence form with large drifts
Wenjia Jing, Yiping Zhang
We study the quantitative homogenization of linear second order elliptic equations in non-divergence form with highly oscillating periodic diffusion coefficients and with large dri…
Uniform convergence for linear elastostatic systems with periodic high contrast inclusions
Xin Fu, Wenjia Jing
We consider the Lame system of linear elasticity with periodically distributed inclusions whose elastic parameters have high contrast compared to the background media. We develop a…
Effective fronts of polygon shapes in two dimensions
Wenjia Jing, Hung V. Tran, Yifeng Yu
We study the effective fronts of first order front propagations in two dimensions () in the periodic setting. Using PDE-based approaches, we show that for every ,…
Convergence rate for the homogenization of stationary diffusions in dilutely perforated domains with reflecting boundaries
Wenjia Jing
We revisit the homogenization problem for the Poisson equation in periodically perforated domains with zero Neumann data at the boundary of the holes and prescribed Dirichlet data…
Layer potentials for Lamé systems and homogenization of perforated elastic medium with clamped holes
Wenjia Jing
We investigate Lamé systems in periodically perforated domains, and establish quantitative homogenization results in the setting where the domain is clamped at the boundary of the…
Effective fronts of polytope shapes
Wenjia Jing, Hung Vinh Tran, Yifeng Yu
We study the periodic homogenization of first order front propagations. Based on PDE methods, we provide a simple proof that for , the class of centrally symmetric polyto…
Generalized ergodic problems: existence and uniqueness structures of solutions
Wenjia Jing, Hiroyoshi Mitake, Hung V. Tran
We study a generalized ergodic problem (E), which is a Hamilton-Jacobi equation of contact type, in the flat -dimensional torus. We first obtain existence of solutions to this p…
A unified homogenization approach for the Dirichlet problem in Perforated Domains
Wenjia Jing
We revisit the periodic homogenization of Dirichlet problems for the Laplace operator in perforated domains, and establish a unified proof that works for different regimes of hole-…
A backscattering model based on corrector theory of homogenization for the random Helmholtz equation
Wenjia Jing, Olivier Pinaud
This work concerns the analysis of wave propagation in random media. Our medium of interest is sea ice, which is a composite of a pure ice background and randomly located inclusion…
Stochastic homogenization of viscous superquadratic Hamilton-Jacobi equations in dynamic random environment
Wenjia Jing, Panagiotis E. Souganidis, Hung V. Tran
We study the qualitative homogenization of second order viscous Hamilton-Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is con…
Inverse problems, non-roundness and flat pieces of the effective burning velocity from an inviscid quadratic Hamilton-Jacobi model
Wenjia Jing, Hung Vinh Tran, Yifeng Yu
The main goal of this paper is to understand finer properties of the effective burning velocity from a combustion model introduced by Majda and Souganidis [19]. Motivated by result…
Fluctuations in the Homogenization of Semilinear Equations with Random Potentials
Guillaume Bal, Wenjia Jing
We study the stochastic homogenization and obtain a random fluctuation theory for semilinear elliptic equations with a rapidly varying random potential. To first order, the effecti…
Limiting distribution of elliptic homogenization error with periodic diffusion and random potential
Wenjia Jing
We study the limiting probability distribution of the homogenization error for second order elliptic equations in divergence form with highly oscillatory periodic conductivity coef…
Homogenization of Randomly Deformed Conductivity Resistant Membranes
Wenjia Jing
We study the homogenization of a stationary conductivity problem in a random heterogeneous medium with highly oscillating conductivity coefficients and an ensemble of simply closed…
Spectroscopic imaging of a dilute cell suspension
Habib Ammari, Josselin Garnier, Laure Giovangigli +2
A rigorous homogenization theory is derived to describe the effective admittivity of cell suspensions. A new formula is reported for dilute cases that gives the frequency-dependent…
Localization, Stability, and Resolution of Topological Derivative Based Imaging Functionals in Elasticity
Habib Ammari, Elie Bretin, Josselin Garnier +3
The focus of this work is on rigorous mathematical analysis of the topological derivative based detection algorithms for the localization of an elastic inclusion of vanishing chara…
Passive Array Correlation-Based Imaging in a Random Waveguide
Habib Ammari, Josselin Garnier, Wenjia Jing
We consider reflector imaging in a weakly random waveguide. We address the situation in which the source is farther from the reflector to be imaged than the energy equipartition di…
Corrector Analysis of a Heterogeneous Multi-scale Scheme for Elliptic Equations with Random Potential
Guillaume Bal, Wenjia Jing
This paper analyzes the random fluctuations obtained by a heterogeneous multi-scale first-order finite element method applied to solve elliptic equations with a random potential. W…
Radiative transfer and diffusion limits for wave field correlations in locally shifted random media
Habib Ammari, Emmanuel Bossy, Josselin Garnier +2
The aim of this paper is to develop a mathematical framework for opto-elastography. In opto-elastography, a mechanical perturbation of the medium produces a decorrelation of optica…
Target Identification Using Dictionary Matching of Generalized Polarization Tensors
Habib Ammari, Thomas Boulier, Josselin Garnier +3
The aim of this paper is to provide a fast and efficient procedure for (real-time) target identification in imaging based on matching on a dictionary of precomputed generalized pol…
Quantitative thermo-acoustic imaging: An exact reconstruction formula
Habib Ammari, Josselin Garnier, Wenjia Jing +1
This paper aims to mathematically advance the field of quantitative thermo-acoustic imaging. Given several electromagnetic data sets, we establish for the first time an analytical…
Corrector theory for MsFEM and HMM in random media
Guillaume Bal, Wenjia Jing
We analyze the random fluctuations of several multi-scale algorithms such as the multi-scale finite element method (MsFEM) and the finite element heterogeneous multiscale method (H…