Abstract:
In this thesis, we examine inverse problems for the sub-elliptic heat
equation with the Cauchy-Dirichlet initial-boundary value condition to determine
the time-dependent control parameter. Consequently, on the Heisenberg group, we
find a time-dependent coefficient of the lowest term of the model along with the
temperature distribution using information from an observation point. Spectral
theory and potential theory techniques are the two that we take into consideration.