Non-autonomous multiplicative perturbations of well-posed linear systems

• Applicant: Dr. Hafida Laasri
• Subject Area: Mathematics
• Term: from 2017 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 395546454

Non-autonomous (or time-varying) linear system theory is modern research area of functional analysis and partial differential equations (PDEs) with boundary control and boundary observation. They are often used to model physical systems whose relevant parameters depend on time. With this proposal, which itself consists of two projects, we aim to investigate the analysis of a class of non-autonomous systems that are governed by non-autonomous multiplicative perturbations. This class is motivated by different fundamental PDEs, such as controlled wave equations, Timoshenko beams or wave equation with structural damping. We will focus on maximal regularity, asymptotic behaviour, well-posedness and some control-theoretical properties such as admissibility. Our approach is based on the theory of well-posed linear systems, form methods and approximation methods. The first project is devoted to a class of systems with energy conservation, whereas linear systems governed by time-dependent sesquilinear forms will be the main subject of the second project.

• DFG Programme: Research Grants
• International Connection: France, Netherlands
• Cooperation Partners: Dr. Bernhard H. Haak; Professor Dr. Hans Johannes Zwart