International Conference on Local and Nonlocal Nonlinear Partial Differential Equations
The International Conference on Local and Nonlocal Nonlinear Partial Differential Equations, sponsored by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, will be held in Shanghai from April 24 to 26, 2015.
Different diffusive effects lead to both local and nonlocal PDEs. There is an extensive and well established understanding of the different aspects of this area that took place mainly in the last fifty and sixty years, which includes an extensive linear theory from analysis and probability, and the deep study of nonlinear issues (calculus of variations, applications to mathematical physics and geometry, fluid dynamics, and phase boundaries to name a few). In recent years, different mathematical issues have emerged that carry a common thread of an underlying non-standard diffusivity effect. Classical examples are, of course, the heat equation where temperature tries to revert to its surrounding values, or Levy processes where probability densities tend to flatten in time by "jumping out" of a given domain proportionally to its local density.
The focus of this Conference is to bring together some experts working in these and related subjects to discuss the most recent advances and challenging open problems for further studies. Specific topics of particular interests are gradient and Schrodinger nonlocal flows in H^s, the integral porous medium equations, the surface quasi geostrophic equations, the nonlinear conservation laws and nonlocal elliptic problems in the studies of population dynamics, conformal geometry and phase boundaries.