This thesis concerns the study of regularisation by noise phenomena for ODEs and PDEs. In particular, it focuses on the use of so called pathwise techniques: our aim is to identify analytical properties, satisfied by typical ...

We prove first- and second-order optimality conditions for sparse, purely time-dependent optimal control problems governed by a quasilinear parabolic PDE. In particular, we analyze sparsity patterns of the optimal controls ...

In this work we are interested in the existence of solutions to parabolic partial differential equations associated to gradient flows which involve the so-called double well potential, which is a nonconvex and nonconcave ...

We perform 3D incompressible two-phase flow simulations of rising droplets. Based on a similar 2D benchmark, a 3D benchmark configuration with two test cases is formulated in which we compare the flow solvers DROPS, NaSt3DGPF ...

When two stable model categories C and D are Quillen equivalent, their homotopy categories Ho(C) and Ho(D) are equivalent as triangulated categories. But is the converse also true?
For the stable homotopy category ...

On the example of the simplest C⁰ spline quarklet construction of [1], we demonstrate the possible reduction of the complexity estimates for the approximation of singularity functions on the unit interval given ......

In this thesis we are concerned with developing a systematic framework for dealing with the Carleson and the Variational Carleson Operators. We extend the framework of outer measure Lp spaces of Do and Thiele to an iterated ...

The goal of this thesis is the analysis of functionals subject to a differential constraint. These functionals appear in minimisation problems which are connected to problems coming from continuum mechanics. In the ...

The formal Hermitean 1-matrix model is shown to be equivalent to an effective field theory. The correlation functions and the free energy of the matrix model correspond directly to the correlation functions and the free ...

This thesis addresses the analysis of an optimal control problem in the context of fracture or damage propagation. The problem formulation is given by a tracking type optimal control problem which is governed by a state ...