On the uniqueness of solutions in inverse problems for Burgers' equation under a transverse diffusion

Abstract

We consider the inverse problems of restoring initial data and a source term depending on spatial variables and time in boundary value problems for the two-dimensional Burgers equation under a transverse diffusion in a rectangular and on a half-strip, like the Hopf-Cole transformation is applied to reduce Burgers' equation to the heat equation with respect to the function that can be measured to obtain tomographic data. We prove the uniqueness of solutions in inverse problems with such additional data based on the Fourier representations and the Laplace transformation.