The last decade has seen vigorous research activity to understand systems involving long-range effects, and to directly incorporate such effects in the modeling and analysis. This research has led to fundamental questions about several classes of nonlocal partial differential equations (PDEs), such as their long-time existence and regularity. Examples that will be discussed in this workshop include the following:
(a) long-range effects that lead to pattern formation in a large number of physical systems;
(b) large scale behavior of groups of animals that lead to the so- called aggregation equations with nonlocal transport terms;
(c) models of the surface temperature of the oceans that lead to equations with nonlocal diffusion due to atmospheric effects;
(d) the use of nonlocal diffusions and energies in image processing.
This workshop will bring together both pure and applied mathematicians with a focus on (i) partial differential equations with nonlocal diffusive and/or transport terms, and their probabilistic interpretations (ii) nonlocal problems in pattern formation and phase transitions and biology, and (iii) nonlocal techniques in image processing.
(University of Texas at Austin)
Rustum Choksi (McGill University)
Luis Silvestre (University of Chicago)
Dejan Slepcev (Carnegie-Mellon University)
Luminita Vese (University of California, Los Angeles (UCLA))