‎In this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎To this end‎, ‎the boundary integral equation method is used‎. ‎Since the resulting system of linea...

∂u ∂t = A ∂ 2 u ∂x2 , u(0, x) = g(x). Moreover, we consider a representation of the solution of this problem as a Poisson integral and study the Cauchy problem for the corresponding inhomogeneous equation. Bibliography: 22 titles.

The abstract Cauchy problem for the non-stationary bulk queue M(t)|M[k, B]|1 Abstract We derived state probability equations describing the queue M (t)| M [k, B]|1 and formulated as an abstract Cauchy problem to investigate by means of the semi-group theory of bounded linear operators in functional analysis. With regard to the abstract Cauchy problem of this queue, we determined the eigenfuncti...

Abstract The Cauchy problem for the inhomogeneous Helmholtz equation with non-uniform refraction index is considered. ill-posedness of this tackled by means variational form mollification. This approach proved to be consistent, and proposed numerical simulations are quite promising.