Nestor Guillen Department of Mathematics University of California at Los Angeles Office: MS 6903 Email: nestor@math.ucla.edu About Research >Teaching 170A   Links Nonlocal Wiki

Math 266E. Winter 2012

Topics in non-local evolution equations

Lectures: MWF 2:00-2:50 pm in MS 6221.
Office hours: Monday 3:30-6:30.



Hamilton-Jacobi equation with critical dissipation.
Supercritical surface quasi geostrophic equation.
Non-local porous medium equation.
Aggregation equation.

Student presentations

Alan Mackey
Bertozzi, Garnett and Laurent. Characterization of radially symmetric finite time blowup in multidimensional aggregation equations.

Elizabeth Tuley
Biler, Karch and Monneau. Nonlinear diffusion of dislocation density and self-similar solutions.

Jason Murphy
Constantin and Vicol. Nonlinear maximum principles for dissipative linear nonlocal operators and applications.

Joseph
Gilboa and Osher. Nonlocal operators with applications to image processing.

Yao Yao
Perthame and Vasseur. Regularization in Keller-Segel type systems and the De Giorgi method.

Will Feldman.
Silvestre. Holder estimates for solutions of integro-differential equations like the fractional Laplace


For the main lectures we will be following mostly these papers.

Bertozzi, Laurent and Rosado. Lp theory for the multidimensional aggregation equation.
Caffarelli and Vazquez. Nonlinear porous medium flow with fractional potential pressure.
Caffarelli and Vazquez. Asymptotic behaviour of a porous medium equation with fractional diffusion.
Silvestre. Eventual regularization for the the slightly supercritical quasi-geostrophic equation.
Silvestre. On the differentiability of the solution to the Hamilton Jacobi equation with critical fractional diffusion.