This thesis concerns scalar reaction-diffusion equations with p-Laplacian type diffusion and different types of continuous reaction. In our general setting, the density-dependent diffusion coefficient allows for degenerations and singularities at equilibria 0 and 1 as well as finitely many jump d...

This dissertation thesis presents our recent results concerning bifurcations in superlinear indefinite problems and in reaction-diffusion systems exhibiting Turing's diffusion-driven instability. All problems in the thesis are studied both by analytical and numerical methods. We divided the...

In this thesis, we study criteria for generalized notions of metric regularity for single-valued and set-valued mappings, such as nonlinear and directional versions and the combination of both. We also study similar generalizations of metric subregularity and semiregularity and we focus...

The goal of this thesis is to summarize our recent results regarding the spatial patterns, periodic orbits and travelling waves of dynamical systems on graphs. We focus on dynamical systems with both discrete and continuous temporal structure and a state space. A strong inter...

This thesis brings an overview of our work concerning solvability and bifurcation in various models of suspension bridges. Our efforts are presented in chronological order. At first, we focus on a one-dimensional damped model of a suspension bridge. We bring a revision of the ...

This doctoral thesis deals with iterative solution of the saddle-point linear systems obtained from discretization of the incompressible Navier--Stokes equations using the isogeometric analysis (IgA) approach. Specifically, it is focused on preconditioners for Krylov subspace methods. One of the goals...

The dissertation thesis is devoted to the study of Fučík spectrum for discrete operators. Considering the fact, that the problem of exploring Fučík spectrum for general discrete operators is still a significant challenge, in this thesis we focus on analyses in regards of a par...

This doctoral thesis deals with application of isogeometric analysis to incompressible turbulent flow problems. The Navier-Stokes equations are the basis for computational modeling of the flow of an incompressible Newtonian fluid. Despite the development of the numerical methods for direct numeri...

The main contribution of the thesis is to extend results in Merino-Pospisil-Sobotka-Sottinen-Vives(2019) regarding alpha-RFSV model and to summarize author's research activities based on published academic articles.

This thesis studies multilevel preconditioners. In the introduction, we cover the theory of multigrid methods. We then connect two interesting topics (BPX additive multigrid and smoothed aggregation method) into a new multigrid approach. We will present a BPX preconditioner in t...

The thesis is devoted to the study of quasilinear parabolic and elliptic problems with diffusion driven by the p-Laplacian. The thesis is devoted into two parts. The first part concerns uniqueness/nonuniqueness and validity/nonvalidity of the strong maximum principle of the solution...

This doctoral thesis deals with geometric modelling in industrial applications. The main goal is to describe the shape of water turbines with the help of modern geometric approaches. Therefore, we apply B-spline/NURBS objects to define hydraulic profiles of water turbines and we pr...

The present thesis is motivated by the study of Chvátal's t_0-tough conjecture. We recall this conjecture in the context of Hamiltonian Graph Theory. We review partial results to the conjecture, and we analyse constructions which provide lower bounds to this conjecture and to s...

The aim of this work is to suggest an expansion of preparation of learning materials designed for university teachers who work with students who have chosen advanced mathematics as an elective, or with high school students who are engaged in mathematics beyond compulsory curriculum...

The present thesis is devoted to the study of mathematical problems related to the Navier-Stokes equations in the context of mathematical rigorous derivation of models and their analysis. In particular we deal with the problem of singular limits in fl uid mechanics for compressible...

This dissertation studies variational methods and compactness conditions used in them. The methods are illustrated on the boundary problems for elliptic equations.

The dissertation thesis presents a commented collection of research articles with results in the analysis of numerical schemes for systems that model viscous compressible fluids. They are mainly based on a pioneering work of Karper, who proved a convergence of a numerical scheme to...

In recent years, the study of quaternions has become an active research area of applied geometry, mainly due to an elegant and efficient possibility to represent using them rotations in three dimensional space. Thanks to their distinguished properties, quaternions are often used i...

The dissertation thesis presents our recent results about the partial dynamic equations on discrete spatial domains (so-called lattices). These problems arise from the modeling of processes on spatially structured environment (e.g., cells, crystal lattices, electronic images). Consequently, we study p...

The goal of this thesis is to analyze several distinct problems regarding graph colorings. To motivate the topic, we first demonstrate that the theory of graph coloring provides useful tools for modeling a wide variety of scheduling and assignment problems. We then introduce basic&...