Speaker: Lassi Paunonen (Tampere University)
Title: Energy Decay in Systems of Partial Differential Equations
Abstract:
Partial differential equations (PDEs) can be connected together to form coupled systems or networks to model different types of interconnected structures. For instance, coupled transport equations can be used to model material flows in pipe networks and networks of beam equations can be used to model truss bridges. In this talk we will focus on analysing the decay of energy in linear coupled PDE systems as time goes to infinity. Our approach is based on mathematical control theory and on representing the PDEs as abstract linear differential equations. Our main result provides an efficient way to derive energy decay rates for a class of linear PDE systems consisting of inherently "stable" and "unstable" parts, such as couplings between heat equations and undamped wave equations. The first part of the talk is relatively general. In the second part we will highlight selected technical aspects of the main result and its proof. The presentation is based on joint work with David Seifert and Serge Nicaise.