Well-posedness of the right-hand side identification problem for a parabolic equation

We study the inverse problem of reconstruction of the right-hand side of a parabolic equation with nonlocal conditions. The well-posedness of this problem in Hölder spaces is established.Досліджєно обернену задачу відновлення правої частини параболiчного рівняння з нелокальними умовами. Встановлено коректність цієї задачі у просторах Гьольдера

The stability of difference schemes of second-order of accuracy for hyperbolic-parabolic equations

AbstractA nonlocal boundary value problem for hyperbolic-parabolic equations in a Hilbert space H is considered. Difference schemes of second order of accuracy difference schemes for approximate solution of this problem are presented. Stability estimates for the solution of these difference schemes are established

A note on the difference schemes for hyperbolic-elliptic equations

The nonlocal boundary value problem for hyperbolic-elliptic equation d2u(t)/dt2+Au(t)=f(t), (0≤t≤1), −d2u(t)/dt2+Au(t)=g(t), (−1≤t≤0), u(0)=ϕ, u(1)=u(−1) in a Hilbert space H is considered. The second order of accuracy difference schemes for approximate solutions of this boundary value problem are presented. The stability estimates for the solution of these difference schemes are established

Parabolic time dependent source identification problem with involution and Neumann condition

A time dependent source identification problem for parabolic equation with involution and Neumann condition is studied. The well-posedness theorem on the differential equation of the source identification parabolic problem is established. The stable difference scheme for the approximate solution of this problem and its stability estimates are presented. Numerical results are given

Numerical solution of the nonlocal boundary value problem for elliptic equations

In the present paper a second order of accuracy two-step difference scheme for an approximate solution of the nonlocal boundary value problem for the elliptic differential equation −v''(t) + Av(t) = f(t), (0 ≤ t ≤ T), v(0) = v(T) + ϕ, T∫0v(s)ds = ψ in an arbitrary Banach space E with the strongly positive operator A is presented. The stability of this difference scheme is established. In application, the stability estimates for the solution of the difference scheme for the elliptic differential problem with the Neumann boundary condition are obtained. Additionally, the illustrative numerical result is provided