Applied Mathematics Colloquium: Dr Justin Webster

Title: Implicit Degenerate Evolution Equations & Bio-Biot Applications

Abstract: In this talk we examine the theory of solutions for implicit, degenerate evolution equations of the form [Bu]'+Au=F. We introduce the problem and motivate two central approaches using matrices in n-dimensions. We then move to the framework of abstract Hilbert spaces, and present the analogous, useful theorems. In the second half of the talk, we describe some exciting biological applications related to organ systems and tissue dynamics. We connect the relevant evolutionary PDE systems to implicit, degenerate evolution equations, for which we can apply the established theory. At the end of the talk we will discuss some very recent work on nonlinear poro-elastic problems, as well as the challenging problem of fluid filtration through poro-elastic tissue (Biot-Stokes coupling).