I am basically only looking for a name of a problem so I can find information about it. A friend of mine explained it to me like this:
Given is a set of string variables $(x_1, \ldots, x_n)$, and a set of regular expressions $(r_1, \ldots, r_n)$ which constrain the string variables $x_i \in \mathbb{L}(r_i)$. Also given are two concatenations $c = x_{c_1} x_{c_2} \ldots x_{c_s}$ and $d = x_{d_1} x_{d_2} \ldots x_{d_t}$ over these string variables. The question now is: are there values for $x_1 \ldots x_n$ s.t. $c = d$?
As an example: Let $x_1, x_2, x_3$ be our string variables, and $a^*a, \ b^*b, \ (a|b) a^*$ our regular expressions respectively. Our concatenations are $c = x_1 x_2 x_1$ and $d = x_3 x_3$. Then $c=d$ is unsatisfiable. If we'd change the regular expression for $x_3$ to $(a|b)^*a$, then $c=d$ would be satisfiable.
Unfortunately, he only knows it as the 'String problem', which doesn't give too much information about it. Is that really it's name? Or how can I find more information about it?