No abstract

In this paper, the initial value problem for the first order partial differential equation with the nonlocal boundary condition is studied. In applications, the stability estimates for the first order partial differential equation with the nonlocal boundary condition are obtained. The finite difference method for the initial value problem for hyperbolic equations with nonlocal boundary conditions is applied. In practice, the stability estimates for the solution of the difference scheme of the problem for hyperbolic equations with nonlocal boundary conditions are obtained.

In this paper, a right‐hand side identification problem for a parabolic equation with an overdetermined condition on an observation point is considered. A first and second order of accuracy difference schemes are constructed for obtaining approximate solutions of the problem that arises in two‐phase flow in capillaries. Stability estimates and numerical results are also established. Copyright © 2013 John Wiley & Sons, Ltd.

The inverse problem of reconstructing the right-hand side (RHS) of a mixed problem for one-dimensional diffusion equation with variable space operator is considered. The well-posedness of this problem in Hölder spaces is established.

A space source of identification problem for parabolic equation with involution and Dirichlet 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 is presented. Furthermore, stability estimates for the difference scheme of the source identification parabolic problem are presented. Numerical results are given.