The observability of Burgers' equation, the Riccati equation, and the heat equation

The question of observability is that of recovering the initial data from a point measurement. This problem has been intensively studied by Martin, Gilliam. Wolf, etc. In this dissertation research we are looking at the observability of Burger's equation via the representation of solutions as ratio of solutions of the heat equation. This extends the work of Martin and Ghosh on the observability of Riccati equation.\n\nAlso we have shown that the boundary data for the one-dimensional heat system given in Chapter II can be determined up to a linear equivalence relation in the Grassmannian manifold G'^{R^) by the spectra which can be recovered from a point observation.\n\nFinally, in Chapter III, we are looking at the explicit solution of the nonlinear Burgers' system.