On some classes of inverse problems for parabolic and elliptic equations
An inverse problem associated with parabolic and elliptic equations is considered. The authors study the solvability of such inverse problems of finding the solution together with some functions on the right-hand-side of the equation, when some supplementary conditions are given. These overdetermination conditions are represented by the values of a solution on some system of surfaces. Problems of this type arise in heat and mass transfer, diffusion and filtration processes. The authors prove that the considered parabolic problem is not always solvable, and they present solvability conditions. Moreover, they show that the problem is always solvable if the overdetermination condition is understood in some generalized sense.
scientific article; zbMATH DE number 5997667
scientific article