I'm trying to solve a problem where I have a initial and final distribution of tumor, and my goal is to find the best map of parameters (diffusion and reaction terms) for a reaction-diffusion equation, which explain at best the final distribution, knowing the initial one.
By doing some literature search, I figured out that the concept I'm dealing with is the so called "pde-constrained optimization problem" and I saw some works using things like "adjoint variables", Lagrangian, etc... that I'm not familiar with.
My problem is that I can't find any good tutorial, online course, or article explaining these concepts and how to use them in practice. Maybe some of you can give me insights about such lesson available ?
I have a fairly background level in mathematics and programmation, so I'm not looking for only understanding "roughly" the field, but indeed being able to apply solutions to my real-life work...
Many thank for any help you can give me...