Bei der Beschreibung von Strömungen wird klassischerweise zwischen inkompressiblen und kompressiblen Bereichen unterschieden. Während inkompressible Strömungen durch ein divergenzfreies Geschwindigkeitsfeld charakterisiert werden, sind kompressible Strömungsfelder durch Expansionsfächer, Kontaktunstetigkeiten und Stoßwellen gekennzeichnet. Die beiden Bereiche werden damit durch stark unterschiedliche Systeme partieller Differentialgleichungen beschrieben. Diese Unterscheidung zeigt sich auch in der numerischen ...

In this dissertation, we analyze an optimal control problem governed by a rate-independent system in an abstract infinite-dimensional setting. The rate-independent system is characterized by a nonconvex stored energy functional, which depends on time via a time-dependent external loading, and by a convex dissipation potential, which is assumed to be bounded and positively homogeneous of degree one. The optimal control problem uses the external load as control variable and is constrained to normalized ...

The dynamics of species concentrations of chemical reaction networks are given by autonomous first-order ordinary differential equations. Singular perturbation methods allow the computation of approximate reduced systems that make explicit several time scales with corresponding invariant manifolds. This thesis presents: 1. An algorithmic approach for the computation of such reductions on solid analytical grounds. Required scalings are derived using tropical geometry. The existence of invariant manifolds is subject ...

In this thesis, we generalize several types of involutive and marked bases for ideals in quotient rings of commutative polynomial rings. We apply these new types of bases to the analysis of infinite free resolutions and of Hilbert schemes defined over certain types of quotient rings. We are mostly concerned with Pommaret and Janet bases; the marked bases we consider are marked over monomial submodules that are quasi-stable, i.e., that possess finite Pommaret bases. Involutive bases of the types we consider induce ...