The first volume of the monograph series “Problems and methods: mathematics, mechanics, cybernetics” contains I.V.Skrypnik’s selected works in which the following questions are studied: A-harmonic forms on a Riemannian manifold, regularity of solutions of quasilinear elliptic high-order equations, topological methods of investigation of solvability of nonlinear equations, quasilinear high-order equations with strengthened ellipticity, regularity of a boundary point for quasilinear equations, point-wise estimates of solutions of model nonlinear problems and homogenization of nonlinear Dirichlet problems in domains with composite structure.

In the second volume of the series  «Problems and methods: mathematics, mechanics,
cybernetics» several trends of investigation of singular solutions of nonlinear elliptic and parabolic equations are covered. Results on existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with  L1-data are stated. Questions on removability of singularities and asymptotic behaviour of solutions in a neighbourhood  of singularity set for general elliptic and parabolic second-order equations in divergence form are considered. Localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form are described.
Annotation and table of contents in English are given at the end of the book.

Mathematical models of some processes of thermal processing of materials are developed on the basis of nonlinear equations of heat mass transfer and free boundary problems. Methods and algorithms for solving the problems of identification of parameters of models are proposed. These ones use ideas of regularization and functional approximation. Algorithms for the control of thermal regime of material processing are developed on a uniform methodological basis. The problem of synthesis of algorithms of disconnected control and control, using operative estimates of thermal state as feedback, is studied. The numerical estimates of the accuracy of synthesized algorithms of filtration and control are obtained.