Publications

Acknowledgements: My works have been supported by 

• • • • 2019-2022, NSFC Grant No. 11871300 (co-PI)

      • 2019-2021, The Recruitment Program of Global Experts of China

      • 2018-2020, NSFC (China) Grant No. 11701314 (PI)

      • 2015-2016, NSF (USA) Grant DMS-1515150 (PI)

Papers and preprints

Note: The preprint versions of papers listed below may be slightly different from the published versions.

1. Quantitative homogenization of state-constraint Hamilton--Jacobi equations on perforated domains and applications. (with Y. Han, H. Mitake and H. V. Tran). [arXiv:2405.01408], submitted.

2. Convergence rate and uniform Lipschitz estimate in periodic homogenization of high-contrast elliptic systems. (with X. Fu). [arXiv:2404.11396], submitted.

3. On the periodic homogenization of elliptic equations in non-divergence form with large drifts. (with Y. Zhang). [arXiv:2302.01157], Multiscale Modeling & Simulations, 21 (2023), no.4, 1486--1501.

4. Uniform convergence for linear elastostatic systems with periodic high contrast inclusions. (with X. Fu). [arXiv:2207.05367], Partial Differential Equations & Applications, 5 (2024), paper no.2, 39 pages.

5. Effective fronts of polygon shapes in two dimensions. (with H. V. Tran and Y. Yu). [arXiv:2112.10747], SIAM J. Math. Anal. 55 (2023), no.6, 6764--6777.

6. Convergence rate for the homogenization of stationary diffusions in dilutely perforated domains with reflecting boundaries. [arXiv:2108.08533] Minimax Theory Appl., 8 (2023) no.  1, 85--108.

7. High order homogenized Stokes models capture all three regimes. (with F. Feppon). [HAL-03098222], Preprint (2021), SIAM J. Math. Anal. 54 (2022), no. 4, 5013--5040.

8. Layer potentials for Lamé systems and homogenization of perforated elastic medium with clamped holes. [arXiv:2007.03333], Calculus of Variations and PDEs. 60 (2021), Paper no.2.

9. Effective Fronts of Polytope Shapes. (with H. V. Tran and Y. Yu). [arXiv:1909.11067], Minimax Theory and its Applications, 5 (2020), no.2, 347--360.

10. Generalized Ergodic Problems: Existence and Uniqueness Structures of Solutions. (with H. Mitake and H. V. Tran). [arXiv:1902.05034], Journal of Differential Equations, 268 (2020), no.6, 2886--2909. 

11. A unified homogenization approach for the Dirichlet problem in perforated domains. [arXiv:1901.08251], SIAM J. Math. Anal. 52 (2020), no. 2, 1192--1220.

12. A backscattering model based on corrector theory of homogenization for the random Helmholtz equation. (with O. Pinaud) [arXiv:1805:02822] DCDS-B,  24 (2019), no.10, 5377--5407.

13. Stochastic homogenization of viscous superquadratic Hamilton-Jacobi equations in dynamic random environment. (with P. E. Souganidis and H. V. Tran). [arXiv:1606.06409] Research in the Mathematical Sciences (2017), Paper No. 6, 20pp.

14. Inverse problems, non-roundedness and flat pieces of the effective burning velocity from an inviscid quadratic Hamilton-Jacobi model. (with H. V. Tran and Y. Yu) [arXiv:1602.04728] Nonlinearity, 30 (2017), no. 5, 1853--1875.

15. Homogenization of interfaces moving in spatially random temporally periodic environment. (with P. E. Souganidis and H. V. Tran). [mathscidoc:1806.03001]Preprint (2016)

16. Fluctuations in the Homogenization of Semilinear Equations with Random Potentials. (with G. Bal) [arXiv:1509.05321] Comm. Partial Differential Equations, 42(2016), no.12, pp. 1839--1859.

17. Limiting distribution of elliptic homogenization error with periodic diffusion and random potential. [arXiv:1505.02721] Analysis & PDE, 9 (2016), no. 1, pp. 193--228.

18. Large time average of reachable sets and Applications to Homogenization of interfaces moving with oscillatory spatio-temporal velocity. (with P. E. Souganidis and H. V. Tran) [arXiv:1408.2013] DCDS-S 11 (2018), no.5, 915--939.

19. Homogenization of Randomly Deformed Conductivity Resistant Membranes, [arXiv:1406.0580] Commun. Math. Sci., 14 (2016), no.5, 1237--1268.

20. Spectroscopic imaging of a dilute cell suspension. (with H. Ammari, J. Garnier, L. Giovangigli and J.K. Seo), [PDF] J. Math. Pures Appl. , 105 (2016), no.5, 603--661.

21. Localization, stability and resolution of topological derivative based imaging functionals in elasticity. (with H. Ammari, E. Bretin, J. Garnier, H. Kang and A. Wahab), [arXiv:1210.6760] SIAM J. Imaging Sci. , 6 (2013), no. 4, 2174-2212.

22. Passive array correlation based imaging in weakly random waveguide. (with H. Ammari and J. Garnier), [arXiv:1211.0682] Multiscale Modeling and Simulation, 11(2013), no.2, pp. 656-681.

23. Corrector analysis of a heterogeneous multi-scale scheme for elliptic equations with random potential. (with G. Bal), [arXiv:1209.4974] Mathematical Modeling and Numerical Analysis (M2AN), 48 (2014), no. 2, 387-409.

24. Radiative transfer and diffusion limits for wave field correlations in locally shifted random media. (with H. Ammari, E. Bossy, J. Garnier and L. Seppecher), [arXiv:1207.1604] , J. Math. Phys. , 54 (2013), 021501.

25. Target identification using dictionary matching of Generalized Polarization Tensors. (with H. Ammari, T. Boulier, J. Garnier, H. Kang and H. Wang), [arXiv:1204.3035] Found. Comput. Math., 14 (2014), no. 1, 27-62.

26. Quantitative thermo-acoustic imaging: an exact formula. (with H. Ammari, J. Garnier and L. Nguyen), [arXiv:1201.0619] J. Differential Equations, 254 (2013), No.3, pp. 1375--1395.

27. Resolution and stability analysis in acousto-electric imaging. (with H. Ammari and J. Garnier), [PDF] Inverse Problems 28 (2012), 084005. 

28. Corrector theory for elliptic equations with oscillatory and random potentials with long range correlations. (with G. Bal, J. Garnier and Y. Gu), [PDF] Asymptotic Analysis, 77 (2012), No. 3-4, pp. 123-145.

29. Corrector theory for MsFEM and HMM in random media. (with G. Bal), [PDF] [Journal] Multiscale Modeling and Simulation 9 (2011), pp. 1549-1587.

30. Corrector theory for elliptic equations in random media with singular Green's function (with G. Bal), [PDF] [Journal] Commun. Math. Sci. 9 (2011), No. 2, pp. 383-411.

31. Homogenization and Corrector Theory for Linear Transport in Random Media (with G. Bal), [PDF] [Journal] Discrete Contin. Dyn. Syst. 28 (2010), No. 4, 1311-1343.

32. Fluctuation theory for radiative transfer in random media (with G. Bal), [PDF] [Journal] Journal of Quantitative Spectroscopy & Radiative Transfer, 112 (2011), No. 4, pp. 660-670.

Book 

1. Mathematical and Statistical Methods for Multistatic Imaging. (with H. Ammari, J. Garnier, H. Kang, M. Lim, K. Solna, and H. Wang), Lecture Notes in Mathematics, Springer-Verlag, Cham, 2013. 

Book Chapters

1. Uncertainty modeling and propagation in linear kinetic equations, (with G. Bal and O. Pinaud), in Uncertainty quantification for hyperbolic and kinetic equations, pp. 59--92, SEMA-SIMAI Springer Ser., 14, Springer, Cham 2017.

Conference Proceedings 

1. On the homogenization of a front propagation model in oscillatory environments, [PDF] Proceedings of the 8th ICCM, submitted.