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In this paper we consider an inverse problem of identification of a right-hand side in a second order parabolic and hyperbolic equations with a parameter. We prove theorems on existence and uniqueness of solutions to these problems. [ABSTRACT FROM AUTHOR]

In this paper the inverse problem of finding the minor coefficient and the inverse problem of finding the right-hand side member of special type in a second order parabolic equation with changing time direction are considered. The existence and uniqueness of solutions to these problems are investigated. [ABSTRACT FROM AUTHOR]

Existence and uniqueness of solution to the inverse problem Bu[subt]+ Lu= ϒ(t)...+ f(t), u(0)=u[sub0], u(T)= u[subT] are investigated. Operators B and L are self-adjoint in a Hilbert space E; the spectrum of the operator L is semibounded; ϒ(t) is a scalar function. If a finite number of orthogonality conditions holds then the inverse problem is uniquely solvable. The method uses the representation as a series in eigenelements and associated elements of the pencil L - λB. [ABSTRACT FROM AUTHOR]