## Research

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# Mathematical modeling

Our group believes that mathematics is the language of Nature. Laws of Nature are typically written as partial differential equations (e.g the heat equation, equations of fluid flow, or wave equation) or as minimization and maximization problems (light takes the path of the least time). We study a wide range of models of real processes and phenomena, we study the existence, uniqueness and stability of their solutions, we search for numerical solutions of these models and we study various methods of their optimization. We cooperate with researchers in physics, chemistry, biology, engineering, economy, medicine and anyone else with a need for a quantitative understanding of their field of study.

We often meet large data sets - digital image data, audio data, various databases of medical or economic nature - and we try to keep in touch with the state-of-the-art mathematical tools of their analysis.

Researchers: Rotislav Vodák, Tomáš Fürst, Horymír Netuka, Pavel Ženčák, Jitka Machalová, Ondřej Vencálek