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The main areas of research are to create new mathematical models of the theory of elasticity, electrodynamics, acoustics, astrophysics, immunology and pharmacokinetics; In the study of the properties of these models and in the study of the possibility of identifying models (the definition and refinement of the main parameters of models, the initial conditions of the processes, sources and regions studied). Numerical investigation of supercomputer models using modern parallel computing technologies is provided. The variety of claimed mathematical models (from pharmacokinetics to astronomy) is combined by equations of mathematical physics and the methodology of investigating inverse problems