The development of operator theory is stimulated by the need to solve problems emerging from several fields in mathematics and physics. At present time, this has wide applications study non-linear differential equations, linear transport theory, diffraction acoustic electromagnetic waves, scattering inverse scattering, among others. In our work, we use computer algebra system Mathematica implem...

in Hilbert space and their realizations in function spaces as initial-boundary value problems for partial differential equations which may contain degenerate or singular coefficients. The Cauchy problem consists of solving (1.1) subject to the initial condition Jdu(0) = h. We are concerned with the case where the solution is given by an analytic semigroup; it is this sense in which the Canchy p...

The sideways parabolic equation (SPE) is a model of the problem of determining the temperature on the surface of a body from the interior measurements. Mathematically it can be formulated as a noncharacteristic Cauchy problem for a parabolic partial differential equation. This problem is severely ill-posed in an L2 setting. We use a preconditioned generalized minimum residual method (GMRES) to ...

Based on a general, operational approach, two new integral identities for the fundamental solutions of the potential and elastostatic problems are established in this paper. Non-singular forms of the conventional boundary integral equations (BIEs) are derived by employing these two identities for the fundamental solutions and the twoterm subtraction technique. Both the strongly(Cauchy type) and...