Prediction of solutions to initial boundary value conjugation problems for parabolic equations with incomplete data
We consider systems described by initial-boundary value problems for parabolic equations with discontinuous coefficients. From observations of the state of systems, we find minimax prediction estimates of functionals from solutions of these initial-boundary value problems at an arbitrary moment of time in the future. It is assumed here that the right hand sides of equations boundary, transmission conditions and also errors of measurements are not determined exactly but only the sets to which they belong are known and that the information concerning initial conditions is missing. It is established that the determination of the aforementioned estimates is reduced to solving some systems of integro-differential equations.