Associate Professor |
Office: 617 Thackeray Hall |

- Nonlinear Partial Differential Equations
- Calculus of Variations
- Geometric Measure Theory
- Geometric Analysis

- NSF Award #1200599, PI: Partial differential equations arising from physical and biological sciences: Singularity and Nonlinearity, 6/01/2012--05/31/2015

- Regularity of a vector valued two phase free boundary problems. Submitted
- Point rupture solutions of a singular elliptic equation. With Attou Miloua, Submitted
- Regularity of Expanding Front and its Application to Solidification/Liquidation in Undercooling Liquid/Superheated Solid, with Xinfu Chen, Submitted
- Traveling Waves of A Non-local Conservation Law.

With Xinfu Chen,*Differential and Integral Equations*,25(11-12): 1143-1174, 2012. - Singular limit of an energy minimizer arising from dewetting thin film model with van der Waal, born repulsion and surface tension forces.

With Xinfu Chen,*Calculus of Variations and PDE*, 44(1-2):221-246, 2012. - Full regularity of a free boundary problem with two phases.

With Christopher Larsen and Luis Silvestre,*Calculus of Variations and PDE*, 42(3-4):301-321, 2011. - Energy Minimizers of a Thin Film Equation with Born Repulsion Force.

*Commun. Pure Appl. Anal.*, 2:803-815, 2011. - Existence and nonexistence of nontrivial steady states of an activator-inhibitor system.

With Wei-Ming Ni,*Variational Problems and Related Topics*, April:143-147, 2008 - On steady states of van der Waals force driven thin film equations.

With Wei-Ming Ni,*European Journal of Applied Mathematics,*18:153-180, 2007 - Analytic regularity of
a free boundary problem.

*Calculus of Variations and PDE*, 28(1):1-14, 2007 - A prior estimates of stationary solutions of an activator-inhibitor system.

With Wei-Ming Ni,*Indiana Univ. Math. J.*, 56(2):681-732, 2007 - A remark on the
existence of suitable vector fields related to the dynamics of scalar
semi-linear parabolic equations.

With Fengbo Hang,*Proceedings of AMS,*134(9):2633-2637, 2006 - Global existence of solutions of an activate-inhibitor system.

*Discrete Contin. Dyn. Syst,*14(4):737-751, 2006 - A new type of free boundary problem with volume constraint.

With Fanghua Lin,*Comm. Partial Differential Equations*, 29(5-6):821-865, 2004 - Zero set of Sobolev functions with negative power of integrability.

With Fanghua Lin,*Chinese Ann. Math. Ser. B*, 25(1):65-72, 2004 - Infinitesimal deformations of surfaces of positive curvature in R
^{3}and some classes of boundary value problems.

*Chinese Ann. Math. Ser. A*, 19(6):659-666, 1998.

- Fall, 2007: Math 0230
- Spring, 2008: Math 0290
- Summer, 2008: Math 1270
- Fall, 2008: Math 0230; Math 1470
- Summer, 2009: Math 1270
- Fall, 2009: Math 0413; Math 2301
- Spring, 2010: Math 1290; Math 2302
- Summer, 2010: Math 1270
- Fall, 2010: Math 2303; Math 1530
- Spring, 2011: Math 2304
- Fall, 2011: Math 0230; Math 0290
- Spring, 2012: Math 0290
- Fall, 2012: Math 0290 ; Math 1470
- Please check courseweb for teaching materials

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