Math 832: Partial Differential Equations II.
The course webpage is on
Blackboard
Math 820: Topics in Nonlinear Analysys: Optimal Transport,
Gradiant Flows, and applications
Description.
The course webpage is on
Blackboard
Publications and preprints
with S. Esedoglu,
Refined Upper Bounds on the Coarsening Rate of Discrete, Ill-Posed
Diffusion Equations,
submitted [.pdf].
Coarsening in nonlocal interfacial systems,
submitted [.pdf].
with K. Glasner, F. Otto, and T. Rump,
Ostwald ripening of droplets: The role of migration,
to appear in European Journal of Applied Mathematics [.pdf].
with R. McCann,
Second-order asymptotics for the fast-diffusion equation,
Internat. Math. Res. Notices 2006, Art. ID 24947, 22 pp.
[.pdf].
with F. Otto and T. Rump,
Coarsening rates in a droplet model: rigorous upper bounds,
SIAM J. Math. Anal. 38 (2006), no. 2, pp. 503-529
[.pdf].
Linear stability of selfsimilar solutions of unstable
thin-film equations,
submitted [.pdf].
with M.C. Pugh,
Selfsimilar blowup of unstable thin-film equations,
Indiana Univ. Math. J. [.pdf] 54 (2005) no. 6 pp. 1697-1738.
with F. da Lio and C.I. Kim,
Nonlocal front propagation problems in bounded
domains with Neumann-type boundary conditions and applications,
Asymptotic Analysis 37 (2004) no. 3-4 pp. 257-292 [.pdf].
On level-set approach to motion of manifolds of
arbitrary codimension, Interfaces and Free Boundaries, 5 (2003)
pp. 417-458 [.pdf].
Aproximation schemes for propagation of fronts with nonlocal
velocities
and Neumann boundary conditions, Nonlinear Analysis,
52 (2003) pp. 79-115 [.pdf].