AN INVERSE PROBLEM FOR A SEMILINEAR PARABOLIC EQUATION

We consider the determination of a function p from overspecified data, where the function p appears in an initial-boundary value problem for the equation partial derivative(t)u-Delta u-pu + f(u) = 0. The main idea in our approach consists of transforming this inverse problem into the problem of finding a solution to a non-standard non-linear equation. Using the classical Holder a priori estimates and the Schauder fixed-point theorem, we find a solution to this equation. This result then enables us to show the existence of a solution to the inverse problem. The continuous dependence of the solution to the inverse problem on the non-linear term, the boundary-value, and the overdetermined data, is also proved. Results for the linear case have already been published by the author.