Assoc. Prof. Dr. Farrukh Dekhkonov | Computational Theory | Best Researcher Award

Associate Professor Farrukh Dekhkonov is a researcher in the field of mathematical physics, focusing on differential equations, partial differential equations, applied mathematics, integral equations, boundary value problems, control theory, and mathematical modeling. His work emphasizes the development and analysis of boundary and time-optimal control problems associated with parabolic and pseudo-parabolic equations, including multi-dimensional domains and systems with involution. By investigating the heating process of rods, plates, and other physical systems, Dekhkonov has contributed significantly to understanding the dynamics of thermal processes and optimal control strategies in various geometries and boundary conditions. His research integrates theoretical analysis with computational methods to design effective control protocols for complex systems, ensuring precise management of heat transfer and diffusion processes. Through rigorous mathematical modeling, he has addressed both classical and novel control challenges, offering solutions for one-dimensional, two-dimensional, and three-dimensional equations of parabolic and pseudo-parabolic types, including periodic and involution-influenced systems. Dekhkonov’s work encompasses time-optimal control, establishing frameworks that minimize the time required to achieve desired system states while adhering to boundary constraints, and extends to the analysis of higher-order parabolic equations. Collaborative efforts have expanded the scope of his research, applying advanced techniques to multi-dimensional and higher-order systems, ensuring the robustness of control strategies across diverse physical models. Contributions to journals such as Discrete and Continuous Dynamical Systems, Communications in Analysis and Mechanics, and Lobachevskii Journal of Mathematics highlight the combination of theoretical innovation and practical application in his research. His investigations provide a foundation for future studies in mathematical control theory, emphasizing efficiency, stability, and adaptability in complex dynamic systems. Farrukh Dekhkonov’s expertise bridges abstract mathematical concepts with applied problem-solving, facilitating advancements in the precise manipulation of thermal and diffusion processes. 126 Citations, 23 Documents, 9 h-index, View h-index