On a certain inverse problem for the heat equation on the circle
This is one of a series of papers by the present author and by others, dealing with the problem of determining the potential q(x) or the potential as well as the initial value u(x,0), in the parabolic equation \(u_ t-u_{xx}+q(x)u=0\). To achieve this, one typically gives some combination of overposed data on characteristic lines. The present paper is concerned with periodic boundary conditions in the space variable and the complicating factor here is the possibility of double eigenvalues. Necessary conditions are given for uniquely determining the potential and the initial data when the values of \(u(x_ i,t)\) and of \(u_ x(x_ i,t)\) are prescribed for various choices of the points \(x_ i\). The proofs will be found in a forthcoming paper.
scientific article; zbMATH DE number 3855625