INVERSE PROBLEM WITH INTEGRAL OVERDETERMINATION CONDITION FOR A HYPERBOLIC EQUATION

In the paper, we study an inverse problem for a hyperbolic equation with integral overdetermination condition. The existence of a generalized solution is proved.

Inverse Problem with Integral Overdetermination for System of Equations of Kelvin-Voight Fluids

In the paper we consider an inverse problem for the three-dimensional nonlinear pseudoparabolic equations describing the Kelvin-Voight motion. The inverse problem consists of finding a velocity field and pressure which is gradient and also a right-hand said of the equation. Additional condition about the solution to the inverse problem is given in the form of integral overdetermination condition. The existence and uniqueness of weak generalized solution of this inverse problem in the sobelev space is proved.

Inverse Problem for Source Function in Parabolic Equation at Neumann Boundary Conditions

The second initial-boundary value problem for a parabolic equation is under study. The term in the source function, depending only on time, is to be unknown. It is shown that in contrast to the standard Neumann problem, for the inverse problem with integral overdetermination condition the convergence of it nonstationary solution to the corresponding stationary one is possible for natural restrictions on the input problem data

Inverse Problems of Finding the Lowest Coefficient in the Elliptic Equation

The article is devoted to the study of problems of finding the non-negative coefficient q(t) in the elliptic equation utt + a2Δu − q(t)u = f(x, t) (x = (x1, . . . , xn) ∈ Ω ⊂ Rn, t ∈ (0, T), 0 < T < +∞, Δ — operator Laplace on x1, . . . , xn). These problems contain the usual boundary conditions and additional condition ( spatial integral overdetermination condition or boundary integral overdetermination condition). The theorems of existence and uniqueness are proved