Energy-based analysis of evolution equations

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Evolution equations describe the temporal development of a dynamical system with a given initial state and a given input. We treat a special class of evolution equations called infinite-dimensional port-Hamiltonian systems and we develop further the energy-based analysis for these systems. Many physical systems can be formulated using a Hamiltonian framework. The class of infinite-dimensional port-Hamiltonian systems is a subclass of well-posed linear systems that includes many examples of partial differential equations (PDEs) with boundary control and boundary observation, such as heat equations, wave equations, Euler-Bernoulli beam equations and Schrödinger equations. We study the qualitative behavior of the solutions of such equations focussing on stability, well-posedness, and control-theoretical properties. Our approach is based on the theory of operator semigroups, spectral theory, well-posed linear systems, and multiplier techniques for PDEs.