EVENT DETAILS AND ABSTRACT

Title: Entropy Solutions to Conservation Laws with Discontinuous Fluxes via Microscopic Interacting Particle Systems
Speaker: Nadine Even
Speaker Info: University of Wuerzburg and Northwestern University
Brief Description:
Special Note:
Abstract:

We are concerned with entropy solutions in $L^\infty$ of a class of scalar conservation laws whose flux functions are discontinuous with respect to the space variable. We identify a suitable, physical relevant notion of measure-valued solutions, which incorporates the discontinuity of the flux functions naturally. We establish the reduction of measure-valued entropy solutions for this class of conservation laws, which implies the strong convergence of corresponding approximate solutions that determine the measure-valued solutions to the entropy solutions in $L^\infty$. With the compactness framework, we establish the existence of entropy solutions, which are also unique, to this class of conservation laws through the convergence of approximate solutions constructed from a microscopic interacting particle system.