Abstract:
We consider the inverse problem of determining unknown functions occurring in boundary conditions together with the solution to the initial-boundary value problem for a second-order parabolic equation. The overdetermination conditions are integrals of the solution with weight. The existence and uniqueness theorem for solutions to this inverse problem is established.
Keywords:inverse problem, parabolic equation, boundary and initial conditions, Sobolev space, existence and uniqueness theorem, solvability.