I'm a William W. Elliott Assistant Research Professor at Duke Mathematics Department. My interest lies in applied math, including
- Mathematical physics (PDE models, optimal transport etc)
- Time fractional differential equations
- Numerical SDEs and PDEs
- Fluid-Structure interaction
2010-2015. Mathematics. Phd. UW-Madison.
Minor: Probability and analysis; Advisor: Saverio Spagnolie
2013. Mathematics. MA. UW-Madison
2012. Computer Science. MS. UW-Madison.
2006-2010. Mathematics and Physics(基科) (applied). BS. Tsinghua University, Beijing.
Large time behaviors of upwind schemes by jump processes
L. Li, J. Liu
On Runge-Kutta methods for the water wave equation and its simplified nonlocal hyperbolic model
L. Li, J. Liu, Z. Liu, Y. Yang, Z. Zhou
Patched peakon weak solutions of the modified Camassa-Holm equation
Y. Gao, L. Li, J. Liu
On the diffusion approximation of nonconvex stochastic gradient descent
W. Hu, C. J. Li, L. Li, J. Liu Annals of Mathematical Sciences and Applications To appear
Semi-groups of stochastic gradient descent and online principal component analysis: properties and diffusion approximations
Y. Feng, L. Li, J. Liu Communications in Mathematical Sciences To appear
Some compactness criteria for weak solutions of time fractional PDEs
L. Li, J. Liu SIAM: Math. Anal. 2018. Vol. 50, Issue 4. 3963-3995
A generalized definition of Caputo derivatives and its application to fractional ODEs
L. Li, J. Liu SIAM: Math. Anal.
2018. Vol. 50, Issue 3. 2867-2900
A dispersive regularization for the modified Camassa-Holm equation
Y. Gao, L. Li, J. Liu SIAM J. Math. Anal.
2018. Vol. 50, Issue 3. 2807-2838
Cauchy problems for Keller-Segel type time-space fractional diffusion equation
L. Li, J. Liu, L. Wang J. Differ. Equations
2018. Vol. 265, Issue 3
A note on one-dimensional time fractional ODEs
Y. Feng, L. Li, J. Liu, X. Xu Applied Mathematics Letters
2018. Vol. 83. pdf file
p-Euler equations and p-Navier-Stokes equations
L. Li, J. Liu J. Differ. Equations
2018. Volume 264, Issue 7
A note on deconvolution with completely monotone sequences and discrete fractional calculus
L. Li, J. Liu Quart. Appl. Math.
2018. Vol. 76, Issue 1
Continuous and discrete one dimensional autonomous fractional ODEs
Y. Feng, L. Li, J. Liu, X. Xu Discrete and Continuous Dynamical Systems- Series B, In press
Fractional stochastic differential equations satisfying fluctuation-dissipation theorem
L. Li, J. Liu, J. Lu J. Stat. Phys.
2017. Vol. 169, Issue 2.
A locally gradient preserving reinitialization for level set functions
L. Li, X. Xu, S. E. Spagnolie Journal of Scientific Computing.
2017. Vol. 71, Issue 1. pdf file
Swimming and pumping by helical waves in viscous and viscoelastic fluids
L. Li, S. E. Spagnolie Physics of fluids.
2015. Vol. 27, Issue 2.
Analytical solution for laterally loaded long piles based
on Fourier-Laplace integral
F. Liang, Y. Li, L. Li, J. Wang. Applied Mathematical Modelling.
2014. Vol. 38. Issue 21 pdf file
The instability of a sedimenting suspension of weakly flexible fibres
H. Manikantan, L. Li, S. E. Spagnolie, D. Saintillan.
Journal of fluid mechanics.
2014. Vol 756. 935-964
Swimming and pumping of rigid helical bodies in viscous fluids
L. Li, S. E. Spagnolie, Physics of fluids.
2014. Vol. 26, Issue 4.
The sedimentation of flexible filaments
L. Li, H. Manikantan, D. Saintillan, S. E. Spagnolie.
Journal of fluid mechanics.
2013. Vol 735. 705-736
Asymptotic and numerical analysis of fluid-structure interactions at different Reynolds numbers.
MATH 660 -Intro. Numer. PDEs, Spring, 2018
MATH 212 -Multivariable Calculus, Fall, 2017
MATH 575 -Mathematical Fluid dynamics, Spring, 2017
MATH 212 -Multivariable Calculus, Fall, 2016
MATH 660 -Intro. Numer. PDEs, Spring, 2016
MATH 212 -Multivariable Calculus, Spring, 2016
MATH 212 -Multivariable Calculus, Fall, 2015
- MATH 319 -Differential Equations, Spring, 2015
- MATH 234 -Calculus, Fall, 2014
- MATH 320 -Linear algebra and differential equations
- MATH 234 -Calculus, Fall, 2013
- MATH 340 -Elem Matrix&Linear Algebra, Spring, 2013
- MATH 321 - Applied Mathematical Analysis, Fall, 2012
- MATH 321 - Applied Mathematical Analysis, Spring, 2012
- MATH 222 - Calculus and Analytic Geometry, Fall, 2011
- MATH 222 - Calculus and Analytic Geometry, Spring, 2011
- MATH 222 - Calculus and Analytic Geometry, Fall, 2010
Notes for my graduate study
Some examples of problems