Date & Time: Monday, July 22, 2013, 15:00-16:00.
Venue: Ramanujan Hall
Title: Dispersion and dissipation with the Hilbert transform: a tale of numerics and analytics
Speaker: Vasudeva Murthy, TIFR Bangalore
Abstract: Nonlocal dispersion and dissipation can be effectively modeled using the Hilbert transform (HT). A typical equation incorporating nonlocal dispersion is the Benjamin-Ono equation. We analyze this equation numerically. The main feature of this study is an effective discretization of the HT. Next we add a dissipation term containing the HT to the Constantin-Lax-Majda model and show analytically that the solution blows up later than with the standard local diffusion term.