In this paper we investigate a problem of the identification of an unknown source from one
supplementary temperature measurement at a given instant of time for the transient heat …

Calderón–Ryaben'kii potentials provide the foundation for the difference potential method,
which is an efficient way for solving boundary-value problems (BVPs) in arbitrary domains …

This work presents the state of the art in the theory of potentials for the solutions of systems
of linear difference equations, which was proposed by the author in 1969. The role played …

We consider the problem of identifying an unknown source which depends on the spatial
variable, in a heat equation. This is an ill-posed problem in the sense that the solution (if it …

We consider the problem of determining an unknown source, which depends only on the
spatial variable, in a heat equation. The problem is ill-posed in the sense that the solution (if …

This paper describes an active sound control methodology based on difference potentials.
The main feature of this methodology is its ability to automatically preserve “wanted” sound …

We formulate and solve a control problem for the field (eg, time-harmonic sound) governed
by a linear PDE or system on a composite domain in Rn. Namely, we require that …

In this note we prove a stability estimate for an inverse heat source problem. Based on the
obtained stability estimate, we present a generalized Tikhonov regularization and obtain the …

We present a methodology for the active control of time-harmonic wave fields, eg, acoustic
disturbances, in composite regions. This methodology extends our previous approach …

We consider active sound control with the preservation of wanted sound in 3D bounded
regions via numerical experiments. In contrast to some previous papers which are based on …