Once limited to modelling physical problems in engineering, today Partial Differential Equations (PDEs) are used by a diverse array of fields, from natural resources to meteorology, aeronautics, oil and gas and biomedicine – to name only a few. But key mathematical issues remain unsolved, particularly when addressing their control, a must in technological transfer. The ERC-funded DYCON project aims to find answers.
A PDE is a model used to describe motion: elastic bodies, fluids, crowds, opinions, etc. It is expressed as an algebraic system involving the partial derivatives of an unknown function and state (depending on space and time variables). PDEs are used to mathematically formulate and describe the motion of the relevant entities in nature and industry, such as heat and sound, fluid flow, elasticity, infections and diseases.
PDEs must be solved and, often times, in practical applications, also controlled, designed and tuned. Prof. Enrique Zuazua explains: “Although there are a range of methods for solving and controlling PDEs, some of the key mathematical issues remain unsolved, thus limiting their applicability to real-life problems”.
Prof. Zuazua and his team of international researchers aim to make a ground-breaking contribution to the broad area of Control of PDEs. To do this, their work focuses on addressing the key unsolved analytical and computational issues in the field. “The coordinated and focused effort that we aim to develop is timely and much needed to solve these issues and will help bridge the gap between PDE control and real applications via computer simulations” says Prof. Zuazua.
The numerous algorithms, tutorials, sample codes, software and simulations developed in the course of the project will all be made available via the DYCON Computational Laboratory. Freely available via the project webpage, these methods and tools have also been released via Zenodo, GitHub and MathWorks.
Enrique Zuazua is the Director of the Chair in Computational Mathematics at DeustoTech Laboratory at the University of Deusto, Bilbao, and a Professor of Applied Mathematics at the Universidad Autónoma de Madrid – UAM (Spain). His fields of expertise, in the broad area of Applied Mathematics, cover topics related to Partial Differential Equations, Systems Control and Numerical Analysis.