# Jian-Guo Liu

## Professor of Physics

### Selected Grants

Collaborative Research: Nonlocal models of aggregation and dispersion awarded by National Science Foundation (Principal Investigator). 2018 to 2021

Collaborative Research: Kinetic Models of Aggregation and Dispersion awarded by National Science Foundation (Principal Investigator). 2015 to 2019

Efficient Numerical Methods for Viscous Incompressible Flows awarded by National Science Foundation (Principal Investigator). 2009 to 2012

Feng, Y, Li, L, Liu, J-G, and Xu, X. "A note on one-dimensional time fractional ODEs." *Applied Mathematics Letters* 83 (September 2018): 87-94.
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Li, L, Liu, J-G, and Wang, L. "Cauchy problems for Keller–Segel type time–space fractional diffusion equation." *Journal of Differential Equations* 265.3 (August 2018): 1044-1096.
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Liu, JG, Tang, M, Wang, L, and Zhou, Z. "An accurate front capturing scheme for tumor growth models with a free boundary limit." *Journal of Computational Physics* 364 (July 1, 2018): 73-94.
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Chen, K, Li, Q, and Liu, J-G. "Online learning in optical tomography: a stochastic approach." *Inverse Problems* 34.7 (July 1, 2018): 075010-075010.
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Liu, J-G, and Xu, X. "Partial regularity of weak solutions to a PDE system with cubic nonlinearity (Accepted)." *JOURNAL OF DIFFERENTIAL EQUATIONS* 264.8 (April 15, 2018): 5489-5526.
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Gao, Y, Liu, J-G, Lu, XY, and Xu, X. "Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface." *Calculus of Variations and Partial Differential Equations* 57.2 (April 2018).
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Liu, J-G, and Xu, X. "Partial regularity of weak solutions to a PDE system with cubic nonlinearity." *Journal of Differential Equations* 264.8 (April 2018): 5489-5526.
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Li, L, and Liu, J-G. "p -Euler equations and p -Navier–Stokes equations." *Journal of Differential Equations* 264.7 (April 2018): 4707-4748.
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Gao, Y, Li, L, and Liu, J-G. "A Dispersive Regularization for the Modified Camassa--Holm Equation." *Siam Journal on Mathematical Analysis* 50.3 (January 2018): 2807-2838.
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Li, L, and Liu, J-G. "A Generalized Definition of Caputo Derivatives and Its Application to Fractional ODEs." *Siam Journal on Mathematical Analysis* 50.3 (January 2018): 2867-2900.
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## Pages

Liu, JG, and Zhang, Y. "Convergence of diffusion-drift many particle systems in probability under a sobolev norm." January 1, 2016. Full Text

Degond, P, Frouvelle, A, and Liu, J-G. "A NOTE ON PHASE TRANSITIONS FOR THE SMOLUCHOWSKI EQUATION WITH DIPOLAR POTENTIAL." 2014.