## Description

In this talk I will discuss Inverse Stefan type free boundary problem for the second order parabolic equation arising for instance, in modeling of laser ablation of biomedical tissues, where the information on the coefficients, heat flux on the fixed boundary, and density of heat sources are missing and must be found along with the temperature and free boundary. New PDE constrained optimal control framework is employed, where the missing data and the free boundary are components of the control vector, and optimality criteria are based on the final moment measurement of the temperature and position of the free boundary. Some numerical results will be shared.

## Date of Event

Thursday, April 11, 2024

## Location

Parker Building Room 338

Optimal Control of Coefficients for the Second Order Parabolic Free Boundary Problems

Parker Building Room 338

In this talk I will discuss Inverse Stefan type free boundary problem for the second order parabolic equation arising for instance, in modeling of laser ablation of biomedical tissues, where the information on the coefficients, heat flux on the fixed boundary, and density of heat sources are missing and must be found along with the temperature and free boundary. New PDE constrained optimal control framework is employed, where the missing data and the free boundary are components of the control vector, and optimality criteria are based on the final moment measurement of the temperature and position of the free boundary. Some numerical results will be shared.

## Presenter Bio

Dr. Hagverdiyev is currently working as a Full-Time Lecturer in the Departmet of Mathematics at the University of Miami. He recently graduated from Florida Institute of Technology with a PhD in Applied Mathematics. He also earned two master's degrees, one from Florida Institute of Technology in Applied Mathematics and another from University of Nottingham in Pure Mathematics along with the bachelor's degree in Applied Mathematics from Baku State University. He worked part time at Texas A&M University, Keiser University and Holyoke Community College before obtaining his PhD.