# Jian-Guo Liu

### **Professor of Physics**

Professor of Mathematics (Joint)

Professor of Mathematics and Physics at Duke Kunshan University

Professor of Mathematics (Joint)

Professor of Mathematics and Physics at Duke Kunshan University

Liu, J. G., et al. “An accurate front capturing scheme for tumor growth models with a free boundary limit.” *Journal of Computational Physics*, vol. 364, July 2018, pp. 73–94. *Scopus*, doi:10.1016/j.jcp.2018.03.013.
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Chen, K., et al. “Online learning in optical tomography: A stochastic approach.” *Inverse Problems*, vol. 34, no. 7, May 2018. *Scopus*, doi:10.1088/1361-6420/aac220.
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Liu, J. G., and X. Xu. “Partial regularity of weak solutions to a PDE system with cubic nonlinearity.” *Journal of Differential Equations*, vol. 264, no. 8, Apr. 2018, pp. 5489–526. *Scopus*, doi:10.1016/j.jde.2018.01.001.
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Li, L., and J. G. Liu. “p-Euler equations and p-Navier–Stokes equations.” *Journal of Differential Equations*, vol. 264, no. 7, Apr. 2018, pp. 4707–48. *Scopus*, doi:10.1016/j.jde.2017.12.023.
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Gao, Y., et al. “Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface.” *Calculus of Variations and Partial Differential Equations*, vol. 57, no. 2, Apr. 2018. *Scopus*, doi:10.1007/s00526-018-1326-x.
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Li, L., and J. G. Liu. “A generalized definition of caputo derivatives and its application to fractional odes.” *Siam Journal on Mathematical Analysis*, vol. 50, no. 3, Jan. 2018, pp. 2867–900. *Scopus*, doi:10.1137/17M1160318.
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Feng, Y., et al. “Semigroups of stochastic gradient descent and online principal component analysis: Properties and diffusion approximations.” *Communications in Mathematical Sciences*, vol. 16, no. 3, Jan. 2018, pp. 777–89. *Scopus*, doi:10.4310/cms.2018.v16.n3.a8.
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Li, L., and J. G. Liu. “Some compactness criteria for weak solutions of time fractional pdes.” *Siam Journal on Mathematical Analysis*, vol. 50, no. 4, Jan. 2018, pp. 3963–95. *Scopus*, doi:10.1137/17M1145549.
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Li, L., and J. G. Liu. “A note on deconvolution with completely monotone sequences and discrete fractional calculus.” *Quarterly of Applied Mathematics*, vol. 76, no. 1, Jan. 2018, pp. 189–98. *Scopus*, doi:10.1090/qam/1479.
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Coquel, F., et al. “Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and glimm front sampling for scalar conservation laws.” *Mathematics of Computation*, vol. 87, no. 311, Jan. 2018, pp. 1083–126. *Scopus*, doi:10.1090/mcom/3253.
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