Multiscale conservation laws driven by Levy stable and Linnik diffusions: asymptotics, explicit representations, shock creation, preservation and dissolution

Dyskretna analiza harmoniczna i niekomutatywna probabilistyka
Osoba referująca: 
Wojbor Woyczyński (Case Western Reserve University)
Data spotkania seminaryjnego: 
czwartek, 23. Maj 2019 - 10:15
We will discuss the interplay between the nonlinear and nonlocal components of the evolution equations. In the particular case of supercritical multifractal conservation laws (CL) the asymptotic behavior, as $t \neq 1$, is dictated by the linearized case. For $\alpha <1$ , the equations driven by infinitesimal generators of Levy -stable diffusions the solution exhibit shocks (for bounded, odd, and convex on R+, initial data) which disappear over a nite time. For Levy -Linnik diffusions, $0 < \alpha < 2$ , the local behavior is strikingly different. The relevant CLs display shocks that do not dissipate over time.