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- Singular limits of Chematoxis model
Nonlinear Anal. TMA vol.46 (2001), 817-834
- Uniqueness and Existence of Hele-Shaw and Stefan problem
Arch. Rat. Mech. Anal. vol 168 (2003) 299-328
- A free boundary problem arising in flame propagation
J. Diff. Equations, vol 191 (2003) 470-489
- Nonlocal front propagation problems in bounded domains with Neumann boundary conditions and applications
with D. Slepcev and F. Da Lio, Asymptotic analysis, vol.37 (2004) 257-292
- Regularity of the
one-phase Hele-Shaw problem,
J. Diff. Equations, vol. 223 (2006) 161-184.
- A free boundary problem with curvature
Comm. PDE. vol. 30 (2005), 121-138.
- Long time regularity of solutions of the Hele-Shaw problem
Nonlinear Anal. TMA, vol.64, (2006), 2817-2831.
- The one-phase Hele-Shaw problem with singularities
with D. Jerison, J. Geom. Anal., vol. 15 (2005), 641-667.
- (survey article) Regularity and speed of the Hele-Shaw flow
Viscosity Solution Theory of Differential Equations and its Developments , RIMS Kokyuroku (Proceedings) vol.1428 (2005), 19-27.
- Regularity properties of initially Lipschitz free boundarys in One-Phase Hele-Shaw problem
with S. Choi and D. Jerison, Amer. J. Math. 129 (2007), no. 2, 527--582.
- Waiting time phenomena for Hele-Shaw and Stefan problems
with S. Choi, Indiana Univ. Math Journal, vol. 55 (2006) 525-552.
- Homogenization of free boundary velocities,
Arch. Ration. Mech. Anal. vol. 185 (2007), 69--103.
- Global-time solutions for a model of contact line motion,
with K. Glasner, Interfaces and Free boundaries. vol. 11 (2009), no.1, 37--60.
- Homogenization of a model problem on contact angle dynamics,
Comm. PDE. vol.33 (2008), no. 7, 1235-1271.
- Locating the first nodal set in higher dimensions,
with S. Choi and D. Jerison, to appear in Transactions of AMS.
- A local regularization theorem on one-phase Hele-Shaw flow,
with S. Choi and D. Jerison, to appear in Indiana Univ. Math. Journal.
- Error estimate on homogenization of free boundary velocities,
to appear in Ann. Inst. Henri Poincare.
- Homogenization of a Hele-Shaw type problem in periodic and random media,
with A. Mellet, to appear in Arch. Ration. Mech. Anal.
- Two-sided Contracting Stefan problem,
with L. Chayes, Comm. PDE. vol. 33(2008) no.12, 2225-2256.
- Homogenization of one-phase Stefan-type problems in periodic and random media,
with A. Mellet, to appear in Transactions of AMS.
- Regularity of one-phase Stefan problem near Lipschitz initial data,
with S. Choi, to appear in American Journal of Mathematics.
- The Supercooled Stefan Problem in One Dimension,
with L. Chayes, to appear in CPAA.
- A gradient flow approach to a free boundary droplet model,
with N. Grunewald, to appear in Calc. Var. and PDE.
- Global existence and uniqueness of solutions to a model of price formation,
with L. Chayes, M. Guandani and M. Gonzalez, to appear in SIAM J. Math. Anal.
- Degenerate diffusion with a drift potential: a viscosity solutions approach,
with H. K. Lei, to appear in DCDS-A. Erratum to the paper is Here
- Viscosity solutions for the two-phase Stefan problem,
with N. Pozar, to appear in Comm. PDE.
- Two phase Stefan-type problem: Regularization near initial data by phase dynamics,
with S. Choi, , to appear in Analysis/PDE
- The Patlak-Keller-Segel model and its variations: properties of solutions via maximum principle,
with Y. Yao, to appear in SIAM J. Math. Anal.
- Global Existence and Finite Time Blow-Up for Critical Patlak-Keller-Segel Models with Inhomogeneous Diffusion,
with J. Bedrossian, to appear in SIAM. J. Math. Anal.
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(survey article) Homogenization and error estimates of free boundary velocities in
periodic media,
to appear in Special Issue ``Analysis and Approximation of
Microstructure Models", Applicable analysis.
- Homogenization of Neumann boundary data with fully nonlinear PDEs,
with S. Choi and K. Lee, to appear in Analysis and PDE.
- Nonlinear Elliptic-Parabolic Problems,
with N. Pozar, submitted.
- Liquid Drops sliding down an inclined plane,
with A. Mellet, to appear in Transactions of AMS.
- An aggregation equation with degenerate diffusion: qualitative property of solutions
with L. Chayes and Y. Yao, to appear in SIAM. J. Math. Anal.
- Homogenization for nonlinear PDEs in general domains with oscillatory Neumann data,
with S. Choi , submitted.
- Dynamic stability of Capillary drops,
with W. Feldman , submitted.
- Quasi-static droplet percolation,
with N. Guillen, submitted.
Inwon C. Kim |