  Differential equation models are crucial to scientific processes. The values
of model parameters are important for analyzing the behaviour of solutions. A
parameter is called globally identifiable if its value can be uniquely
determined from the input and output functions. To determine if a parameter
estimation problem is well-posed for a given model, one must check if the model
parameters are globally identifiable. This problem has been intensively studied
for ordinary differential equation models, with theory and several efficient
algorithms and software packages developed. A comprehensive theory of algebraic
identifiability for PDEs has hitherto not been developed due to the complexity
of initial and boundary conditions. Here, we provide theory and algorithms,
based on differential algebra, for testing identifiability of polynomial PDE
models. We showcase this approach on PDE models arising in the sciences.
