The areas of my research are in the field of nonlinear partial
differential equations.
I have been primarily concerned with two different types of problems:
free boundary problems arising in the mathematical description of
phase
transitions - the so called Stefan problem with surface tension -
and kinetic equations arising in the description of the dynamics
of galaxies -
the so called Vlasov-Poisson and the relativstic Vlasov-Poisson system.
A constraint variational problem arising in stellar dynamics.
Quart. Appl. Math. 65, 145-153 (2007) arXiv:math-ph/0603025v1
(with
Gerhard Rein)
Global existence and nonlinear stability for the relativistic
Vlasov-Poisson system in the gravitational case.
Indiana Univ. Math. J. 56, 2453-2488 (2007)
The original publication is available
here. arXiv:math-ph/0607012v1
(with
Yan Guo)
Stability in the Stefan problem with surface tension (I).
Commun. Partial Differential Eqns. 35 (2), 201-244 (2010) arXiv:0801.1083v1
(with
Govind Menon)
Gradient flow structure for domain relaxation in Langmuir films.
To appear in Quart. Appl. Math. arXiv:1009.0226
Orthogonality conditions and stability in the Stefan problem with surface
tension.
Arch. Rational Mech. Anal.
Volume 203, Issue 3, Page 719-745 (2012) arXiv:1101.5177v1
Instability of stationary spheres in the Stefan problem with surface
tension. .pdf
Spring 2012: Recitation leader, MIT.
Course:
18.03. - Differential Equations.
Instructor: Prof. Haynes Miller
Time and place:
Section r09: Tuesday 11am-12pm, Thursday 11am-12pm, room 24-115
Section r15: Tuesday 12-1pm, Thursday 12-1pm, room 24-115
Past Teaching
Fall 2011: Recitation leader, MIT.
Course:
18.02. - Multivariable
Calculus
Instructor: Prof. James McKernan
Time and place:
Section r04: Monday 10-11am, Wednesday 10-11am, room
4-261
Section r06: Monday 11-12am, Wednesday 11-12am, room 4-261
Spring 2011: Instructor, University of Zurich.
Course:
Selected topics in Analysis.
Time and place: Wednesday, 15.00-17.00, Y27H46
Fall 2010: Teaching Assistant, University of Zurich.
Course:
Analysis I.
Instructor:
Prof. Camillo DeLellis
Time and place: Tuesday, 8:00-9:45, Y27-H12
Language of instruction: German
Spring 2008: Teaching Assistant, Brown University.
Course: AM33 - Methods of Applied Mathematics I.
Instructor:
Prof. Yan Guo
Fall 2007: Teaching Assistant, Brown University.
Course: AM35 - Methods of Applied Mathematics I.
Instructor: Prof.
Hongjie Dong