Linear hyperbolic systems on networks: well-posedness and qualitative properties

Well{posedness of Stiff Hyperbolic Systems

The theory of stii well{posedness of initial value problems for hyperbolic systems with large relaxation terms is reviewed. Furthermore, an asymptotic expansion of solutions with respect to the relaxation parameter is presented. Finally, the theory is illustrated with an example and an outlook concerning boundary value problems is given.

Well-posedness for Hyperbolic Problems

On solution concepts and well-posedness of linear relay systems

In this paper we study the well-posedness (existence and uniqueness of solutions) of linear relay systems with respect to two di5erent solution concepts, Filippov solutions and forward solutions. We derive necessary and su7cient conditions for well-posedness in the sense of Filippov of linear systems of relative degree one and two in closed loop with relay feedback. To be precise, uniqueness of...

Stii Well{posedness for Hyperbolic Systems with Large Relaxation Terms

The Cauchy problem for linear constant{coeecient hyperbolic systems u t + Au x = (1==)Bu is analyzed. Here (1==)Bu is a large relaxation term, and we are mostly interested in the critical case where B has a non{trivial nullspace. A concept of stii well{posedness is introduced that ensures solution estimates independent of 0 < 1. Under suitable assumptions, we prove convergence of the L 2 {solut...

Linear complementarity systems: modelling power and well-posedness

Technological innovation pushes towards the consideration of dynamical systems of a mixed continuous and discrete nature, which are called “hybrid systems.” Hybrid systems arise, for instance, from the combination of an analog continuous-time process and a digital timeasynchronous controller. Many consumer products (cars, micro-wave units, washing machines and so on) are controlled by digital e...