The Department of Mathematics & Statistics would like to welcome:
Dr. Matthew Fury, Penn State Abingdon, on Tuesday, November 11 at 12:30 pm in SCP 229
Title: Ill-posed problems and the irreversibility of heat flow
Abstract: Imagine letting a drop of colored dye fall into a tube of water. Fick’s law of diffusion states that the dye will move from regions of high concentration to regions of low concentration at a certain rate. Similarly, the flow of heat in a given region is governed by the same law. These physical laws are interpreted mathematically by the diffusion equation which can be solved if an initial concentration is known. But what if the process is reversed? If we know the concentration at some fixed time t=T, can we determine how the concentration changed during earlier times leading up to T? Our discussion will explain why this problem is essentially unsolvable, and lead to an investigation of a more general topic of mathematical research known as ill-posed problems.