The classical reaction-diffusion equation can be stated as the rate of change of the state variable $u$ equals the sum of a diffusion operator and a (often nonlinear) reaction term: $u_t = -L\,u + f(u)$, where typically $-L$ is an elliptic operator. The equation, while known in form, can have specific parameters undetermined; for example coefficients in $L$ or the function $f$ itself.
We look at various models for recovery of these but we also do so in a context beyond Brownian motion diffusion and its parabolic pde format. These so-called anomalous diffusion models give rise to nonlocal differential operators of fractional type and add further difficulties to an already complex problem.
The work is joint with Barbara Kaltenbacher.