Size of Nodal Sets for Solutions of Parabolic PDEs

Professor Igor Kukavica, Department of Mathematics, University of Southern California

Space oscillations of solutions are measured by the number of sign changes in one space dimension and by the volumes of the nodal or other level sets. In this talk, we will summarize results involving upper bounds on these quantities. We will address linear and semi-linear equations of parabolic type with emphasis on the Navier-Stokes system.