# Mathematical Biology Seminar

### Mark Allen

Department of Mathematics, University of Texas at Austin

#### The two-phase parabolic Signorini problem

#### Wednesday, July 16, 2014, at 3:05pm

LCB 219

In this talk we will review some obstacle-type problems and their applications.
Particular focus will be given to the thin obstacle problem which in some instances is the
same as the so-called Signorini problem which has applications in biology and finance.
We will then formulate the two-phase parabolic Signorini problem which has its own
applications. We will show how the two phases in this problem cannot touch. This
separation of the phases leads to a proof of the optimal regularity of the solution.