Friday, June 24, 2016 - 9:00am - 9:50am
Peter Constantin (Princeton University)
I will describe results concerning the behavior of solutions of evolution equations with nonlocal dissipation and/or nonlocal forcing, including the Surface Quasi-Geostrophic equation and models of electroconvection.
Friday, March 18, 2016 - 9:00am - 9:30am
Ekkehard Sachs (Universität Trier)
In this talk we consider modern developments of the neoclassical growth model developed by Ramsey almost 90 years ago. One example is the extension to peer-to-peer banking, which leads to a vector optimization problem. Another aspect we consider is the extension of the model with a finite number of households which leads to an optimal control problem with partial differential equations including nonlocal effects. We give theoretical results obtained from optimal control and compare it to their economical interpretation supported by numerical results.
Wednesday, October 30, 2013 - 11:30am - 12:20pm
Richard Lehoucq (Sandia National Laboratories)
A vector calculus for nonlocal operators is developed, including the definition of nonlocal divergence, gradient, and curl operators and the derivation of the corresponding adjoint operators. Nonlocal analogs of several theorems and identities of the vector calculus for differential operators are also presented. Relationships between the nonlocal operators and their differential counterparts are established, first in a distributional sense and then in a weak sense by considering weighted integrals of the nonlocal adjoint operators.
Tuesday, December 4, 2012 - 10:15am - 11:05am
Wan-Tong Li (Lanzhou University)
In this talk, we shall consider some aspects of nonlocal dispersal equations. First, we will present some relations between local (random) and nonlocal dispersal problems and then report our recent results on traveling waves and entire solutions of nonlocal dispersal equations. This talk is based on some joint works with Yu-Juan Sun, Zhi-Cheng Wang and Guo-Bao Zhang.
Monday, December 3, 2012 - 3:15pm - 4:05pm
Michael Herrmann (Universität des Saarlandes)
In this talk we study a class of nonlocal and non-autonomous Fokker-Planck
equations that has recently been introduced
in order to describe the hysteretic behaviour of many-particle systems with dynamical control.
Relying on methods from asymptotic analysis we identify several parameter regimes
and derive reduced evolution equations for certain macroscopic quantities.
In particular, we discuss the fast reaction regime, which
can be understood by adapting Kramers formula for large deviation, and
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