Li Wang

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Research interests

Numerical methods, applied analysis, and mathematical modeling for conservation laws, kinetic theory, quantum mechanics, fluid dynamics, social science, and biology.



Stability of inverse transport equation in diffusion scaling and Fokker-Planck limit (with K. Chen and Q. Li), submitted. [arXiv:1708.03063].

An accurate front capturing scheme for tumor growth models with a free boundary limit (with J.-G. Liu, M. Tang and Z. Zhou), submitted. [arXiv:1708.08395].

A new numerical approach to inverse transport equation with error analysis (with Q. Li and R. Shu), submitted. [arXiv:1708.01984].

Analysis and computation of some tumor growth models with nutrient: from cell density models to free boundary dynamics (with J.-G. Liu, M. Tang and Z. Zhou), submitted. [preprint].

An asymptotic-preserving scheme for kinetic equation with anisotropic scattering: heavy tail equilibrium and degenerate collision frequency (with B. Yan), submitted. [preprint]

Modeling and simulations of particle-laden flow with surface tension (with A. Mavromoustaki, J. Wong and A. L. Bertozzi), submitted. [preprint]


Stability of stationary inverse transport equation in diffusion scaling (with. K. Chen and Q. Li), Inverse Problems, to appear. [arXiv:1703.00097]

Uniform regularity for linear kinetic equations with random input based on hypocoercivity (with Q. Li), SIAM J. Uncer. Quan., to appear. [arXiv: 1612.01219]

Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations (with J.-G. Liu and Z. Zhou), Math. Comp., to appear. [preprint]

Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and Glimm front sampling for scalar hyperbolic conservation laws (with F. Coquel, S. Jin and J.-G. Liu), Math. Comp., to appear. [preprint]


Implicit asymptotic preserving method for linear transport equation (with Q. Li), Comm. Comput. Phys. 22, issue 1, 157--181, 2017. [link]

Efficient numerical schemes for multiscale crowd dynamics with emotional contagion (with M. Short and A. L. Bertozzi), Math. Models Methods Appl. Sci. 27, no. 1, 205--230, 2017. [link]

An asymptotic-preserving scheme for linear kinetic equation with fractional diffusion limit (with B. Yan), J. Comput. Phys. 312, 157--174, 2016. [link]

The ADI methods for two-dimensional nonlinear multidelay parabolic equations (with Q. Zhang, C. Zhang), J. Comp. Appl. Math. 306, 217--230, 2016.

An asymptotic-preserving scheme for the semiconductor Boltzmann equation with two-scale collisions: a splitting approach (with J. W. Hu and S. Jin), Kinetic and Related Models 8, 707-723, 2015. [link]

Rarefaction-singular shock solution for conserved volume gravity driven particle-laden thin film (with A. Mavromoustaki, A. L. Bertozzi, G. Urdaneta and K. Huang),  Phys. Fluids 27, 033301, 2015. [link]

An asymptotic-preserving scheme for the semiconductor Boltzmann equation toward the energy-transport limit (with J. W. Hu), J. Comput. Phys. 281, 806 - 821, 2015. [link]

Contagion shocks in one dimension (with A. L. Bertozzi, J. Rosado, and M. Short),  J. Stat. Phys. 3, Vol. 158, 647 - 664, 2015. [link]

Well-posedness and singular limit of a semilinear hyperbolic relaxation system with a two-scale discontinuous relaxation rate (with F. Coquel, S. Jin, and J. G. Liu),  Arch. Rat. Mech. Anal. 214, 1051-1084, 2014. [link]

Shock solutions for high concentration particle laden thin films (with A. L. Bertozzi),  SIAM J. Appl. Math., 74(2), 322 - 344, 2014. [link]

Asymptotic-preserving numerical schemes for the semiconductor Boltzmann equation efficient in the high field regime (with S. Jin),  SIAM J. Sci. Comp. 35, B799 - B819, 2013. [link]

A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations (with S. Jin and J. G. Liu),  Math. Comp. 82, 749 -779, 2013. [link]

An asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system in the high field regime (with S. Jin) Acta Mathematica Scientia 31, 2219-2232, 2011. Special issue in honor of Peter Lax's 85th birthday. [link]