Publications

• On the structure of entropy solutions of multidimensional systems of conservation laws, Submitted.
• Existence of traveling wave solutions of a high-order nonlinear acoustic wave equation, with M. Chen and T. Walsh, Submitted.
• Characterizations of the existence and removable singularities of divergence-measure vector fields, with N.C. Phuc, Indiana University Mathematics Journal, Volume 57, Number 4, 1573-1598, 2008.
• Gauss-Green theorem for weakly differentiable vector fields, sets of finite perimeter, and balance laws, with G.Q. Chen and W. Ziemer, Communication on Pure and Applied Mathematics, 2008 (to appear).
• Finite element methods for non-linear acoustics and fluids, with Timothy Walsh, Journal of Computational Acoustics, Vol. 15, No. 3, 353-375, 2007.
• Measure-theoretic analysis and non-linear conservation laws, with G.Q. Chen and W. Ziemer, Pure and Applied Mathematics Quarterly, 3 (3), 841-879, 2007.
• Divergence-measure fields, sets of finite perimeter and conservation laws, with G.Q. Chen, Arch. Rat. Mech. Anal.,175,. no.2 245-267, 2005.
• Level set methods to compute minimal surfaces in a medium with exclusions (voids)., with D. Chopp and T. Walsh, Interfaces Free Bound. {\bf 7} (2005), no.~2, 161--185.
• Plane-like minimal surfaces in periodic media with exclusions, SIAM J. Math. Anal. 36 (2004), no. 2, 523--551. ,
• Generalized Snell's law for weighted minimal surfaces in heterogeneous media, with L. Zhilin, L. Xiaobiao and H.Zhao, Methods Appl. Anal. 10 (2003), no. 2, 199--214.

Research grants

• Divergence-measure fields and nonlinear conservation laws, National Science Foundation (Analysis), DMS-0540869.
• PRF Summer Faculty Award, 2008.

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