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A part of our work targets at providing theoretical foundations for kinetic equations
01
Boundary layer analysis
Boundary layer analysis
How do particles interact with the boundary and how does the boundary singularity decay in space inside the domain?
A numerical method for coupling the BGK model and Euler equations through the linearized Knudsen layer. H. Chen, Q. Li and J. Lu. J. Comput. Phys., 398, 2019
Second-order diffusion limit for the phonon transport equation – asymptotics and numerics. A. Nair, Q. Li and W. Sun, PDE and Applications, 3(38)
A convergent method for linear half-space kinetic equations. Q. Li, J. Lu, and W. Sun. ESAIM Math. Model. Numer. Anal., 51(5): 1583-1615, 2017.
Half-space kinetic equations with general boundary conditions. Q. Li, J. Lu, and W. Sun. Math. Comp., 86, 1269-1301, 2017
Validity and regularization of classical half-space equations. Q. Li, J. Lu, and W. Sun. J. Stat. Phys. 166, 398 – 433, 2016.
Diffusion approximations of linear transport equations: asymptotics and numerics. Q. Li, J. Lu, and W. Sun. J. Comput. Phys. 292, 141–167, 2015.
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Derivation of multiscale limit
Derivation of multiscale limit
We derive and numerically verify asymptotic limiting equations for certain systems, including the Schroedinger equation with varying effective mass, and quantum systems with degenerate spectral.
Classical limit for the varying-mass Schrodinger equation with random inhomogeneities. S. Chen, Q. Li and X. Yang. J. Comput. Phys., 438, 2020
A multi-band semiclassical model for surface hopping quantum dynamics. L. Chai, S. Jin, Q. Li, and O. Morandi. SIAM-Multiscale Model. Simul. 13(1), 205-230, 2015.
Semi-classical models for the Schrodinger equation with periodic potentials and band crossings. L. Chai, S. Jin, and Q. Li. Kinet. Relat. Models., 6(3), 505–532, 2013.
03
Well-posedness theory
Well-posedness theory
Boltzmann and its variation equations are shown to be well-posed in a bounded domain, under small time and small boundary variation conditions.
Local Well-Posedness of Vlasov-Poisson-Boltzmann Equation with Generalized Diffuse Boundary Condition. H. Chen, C. Kim and Q. Li. Journal of Statistical Physics, 179, 2020
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