I'm looking for some interesting questions and maybe open problems in inverse problems theory, especially in the framework of **parabolic PDEs** (basically the heat equation). As key words here we can cite for instance:


1) Carleman estimate (to prove uniqueness and stability results).


2) Regularization theory (to regularize ill-posedness).


If someone knows any interesting questions or open problems it would be helpful to list it here. Any recommendation of surveys papers is welcome.



Interesting questions for inverse parabolic problems
[Inverse Problems for Partial Differential Equations](https://books.google.nl/books?id=K_aNMWE5O38C) (third edition, 2017) by Victor Isakov concludes each chapter with a collection of open research problems. Chapter 9 is specifically devoted to inverse parabolic problems. I reproduce one of the "open problems" from that chapter:


![](https://ilorentz.org/beenakker/MO/Isakov.png)


