How to implent a time dependent poisson eqution with a source term, that is described by a differential equation?

[A.Sourais]

Hello,
This approach from @kamensky might be helpful :

Combine a set of PDE with a fenics mechanics package

One approach that is straightforward, albeit perhaps difficult to optimize for large problems, is to just add the ODE system unknowns as “Real”-type components of a mixed space, i.e., global constants. Consider a contrived example (which I just made up for a code demonstration, rather than to be a reasonable model any physical system). The PDE problem is: Find u:\Omega\to\mathbb{R} such that \begin{array}{lr} \partial_t u - c_1\Delta u = 0 & \text{ on }\Omega\text{ ,}\\ c_1\partial u/\parti…