Abstract:
Under examination is the question on existence and uniqueness of solutions to some inverse problems for a parabolic equation. We look for a solution of this equation and a coefficient with the use of the data of an initial-boundary value problem and the Cauchy data on a part of the boundary of a spatial cylindrical domain. A solution is sought in Sobolev spaces and the coefficient in the class of continuous functions.
Keywords:inverse problem, second order parabolic equation, boundary value problem, overdetermination condition.