CANCELLED Grad Student Seminar - Alejandro Santacruz (Math)

Title: The compensated compactness method applied to a system of balance laws

Speaker: Alejandro Santacruz Hidalgo 

Abstract: Systems of balance laws are composed by partial differential equations in the form u(x,t)_t−F(u)_x=g, where u(x,t) is a vector valued function usually interpreted as densities of quantities balanced in a physical system. When the function F is non-linear these systems usually have no classical solution, a standard method used to prove the existence of weak solutions is to study an approximated perturbed system, solve it, and then form a sequence of solutions converging to a solution for the original problem. When the flux function F is non-linear, proving the weak continuity of the flux is a major source of complications, this is where the compensated compactness method can be applied for some of this systems. In this talk I will give an example of a system associated with the ARG (Aw-Rascle-Greenberg) traffic model whose solution can be proven using this method and I will briefly explain each major step in its application. No previous knowledge in PDE's will be assumed.

As always, great food, coffee and drinks will be provided! 

We hope to see you all this Friday! We encourage your participation in the seminar to provide continuity to this project.

You can visit the Grad Seminar website at https://uwomathgrad.github.io/editions/winter2020/