Typical problems with solutions characterised by first-kind discontinuities occurring at interfaces of layered inhomogeneous media are considered with respect to second-order differential equations in partial derivatives. Direct, inverse and mixed types of solution discontinuities are considered. Presented are generalised formulations of problems under consideration, having discontinuous solutions and allowing a uniform description of the processes of heat, mass and charge transfer in multilayer media. Homogeneous difference schemes built on the basis of generalised solutions, which are illustrated by test problems with analytical solutions, are given.
