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Information × Registration Number 0225U002037, (0119U102089) , R & D reports Title Application of modern mathematical methods in fluid dynamics and medicine popup.stage_title Застосування сучасних математичних методів в задачах гідродинаміки та медицини Head Taranets Roman M., Доктор фізико-математичних наук Registration Date 16-02-2025 Organization Institute of Applied Mathematics and Mechanics National Academy of Science of Ukraine popup.description1 Application of modern mathematical methods and approaches to solve problems that appear in modeling of various processes in fluid dynamics, materials science, medicine and biology. popup.description2 The research object is differential equations and systems. The aim of project is to apply modern mathematical methods and approaches to solve problems arising in the modelling of various processes in hydrodynamics, materials science, medicine, and biology. The research methods used include the energy and entropy a priori estimate methods, qualitative theory of differential equations, and fractional analysis techniques to solve the corresponding problems. Several interesting results were obtained during the research, including a qualitative analysis of a mathematical model describing stress occurrence in humans; the existence of solutions for a Kimura-type model describing the spread of epidemics; the qualitative behaviour of solutions for equations with anomalous diffusion and memory; and the influence of rheological properties on the hydrodynamic characteristics of blood flow in the human arterial system and heart. All results are new, relevant, and mostly theoretical. They utilize and further develop modern mathematical methods and approaches and align with global standards. Some of the findings can be incorporated into university courses on modern differential equation theory. Additionally, under certain conditions of economic development, parts of the research may be applicable in relevant medical institutions and industrial. It is important to note that the research is not final, and many questions remain open, requiring further study. Product Description popup.authors Yevhenieva Yevheniia O. Vasylieva Nataliia V. Krasnoshchok Mykola V. Overko Vitalii S popup.nrat_date 2025-02-16 Close