On the inverse problem for a heat-like equation

Abstract

Using the integral representation of the solution of the boundary value problem for the equation with one time-dependent coefficient at the highest space-derivative three inverse problems are solved. Depending on the property of the coefficient we consider cases when the equation is of the parabolic type and two special cases of the degenerate/mixed type. In the parabolic case the corresponding inverse problem is reduced to the nonlinear Volterra integral equation for which the uniqueness of the solution is proved. For the special cases explicit formulae are derived. Both “minimal” and overspecified boundary data are considered.