Join the Department of Mathematics, Applied Mathematics, and Statistics (MAMS) on Tuesday October 16, 2018 for an Analysis and Probability Seminar given by Dr. Wojbor Woyczynski, Professor, CWRU Department of MAMS. Dr. Woyczynski will speak on “Multiscale Conservation Laws Driven by L/’evy Stable and Linnik Diffusions: Asomptotics, Explicit Representations, Shock Creation, Preservation, and Dissolution.” The seminar will be held in Yost 306, from 2:30 – 3:30 PM.
Abstract: Asymptotic behavior of supercritical multifractal fractal conservation laws (CLs) with $L_1$ initial conditions is dictated by the linearized case. Thus obtaining explicit solutions of the latter is of interest. For $ \alpha< 1 $, CLs driven by L\’evy $\alpha$-stable diffusions exhibit shocks for bounded, odd, and convex on $R^+$, initial data. For L\’evy $\alpha$-Linnik diffusions,$0<\alpha\le 2$, the local behavior is strikingly different. The relevant CLs display shocks that do not dissipate over time while those for $\alpha$-stable diffusion ($0<\alpha\le 1$) do.