PDEs on graphs vs. continuous PDEsDavid IngermanMIT
December 13,

ABSTRACT


If a PDE model of a diffusion or a wave is observed at a finite number of points, is it possible to distinguish between a classical continuous PDE and a PDE (difference equation) on a graph? In other words, do finite restrictions of solutions of differential and difference equations coincide? I will talk about examples that suggest that the answers are no and yes, and about applications to inverse problems (determining the type and coefficients of an equation from its solutions) and to numerical approximations of continuous PDEs. The constructions of difference equations on planar graphs matching continuous diffusion and wave equations involve study of totally positive matrices, pseudoline arrangements, rectanglizations and various continued fractions. I will teach a special topics class around the above this spring. The talk will be practically selfcontained and graduate and undergraduate students are welcome. 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

