Karlstad Applied Analysis Seminar (KAAS)

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Future seminars:

A day in Functional Analysis and Applications

When: 10 March 2026, 09:15-14:45
What: Workshop with assorted talks (Book of Abstracts)
Where: 21A3345 and online:  https://kau-se.zoom.us/j/61616693592

When: 22 April 2026, 15:00-15:45
What: Finite volume schemes for a conservative hydrodynamic limit of the Kac-Blume-Capel model: Convergence, parameter stability and simulation
Who: Nicklas Jävergård, Karlstad University
Where: https://kau-se.zoom.us/j/61616693592

Morphology formation in thin films produced from a ternary solution is crucial
for the performance of organic solar cells. Both the separation of excitons into
free charges as well as the charge transport that follows depend on the shape
and connectivity of the distinct polymer regions (the morphology). In this thesis,
we study morphology formation from two different perspectives: A lattice-based
Blume-Capel model with Kawasaki dynamics, and then a continuum system of
coupled parabolic equations with nonlinear and nonlocal drift. The objective of this
licentiate thesis is to represent morphology formation in three space dimensions
using these two models. We relate our work to previous two-dimensional results
for different parameter regimes. At the technical level, we construct a semi-discrete
finite volume scheme to approximate the weak solution of our continuum model
and implement it in Julia. We prove a convergence result of our semi-discrete
scheme as well as a stability result of the weak solution with respect to temperature
variations - a key parameter in the model. Looking at both the lattice model and the
continuum parabolic system, we quantify and compare growth rates of the formed
domains. Finally, we perform numerical experiments confirming convergence of
our scheme and the effect of parameters on the obtained solution. These results
provide a solid foundation for future extensions, including the evaporation of a
mixture component.

When: 28 April 2026, 15:00-15:45
What: From Bulk to Boundary: Heterogeneity in Nonlocal Models
Who: Petronella Radu, University of Nebraska-Lincoln, USA
Where: https://kau-se.zoom.us/j/61616693592

The emergence of nonlocality as a successful framework for capturing a variety of different physical phenomena has catalyzed research in many directions at the applied, computational, as well as at the theoretical levels. While models formulated with the classical continuum mechanics theory have brought huge developments in technology and science over the last century, the new frontier requires tackling discontinuous, singular, or irregular behavior encountered in many applications such as deformations and damage of solid bodies, phase transitions and image processing. To this end, the study of systems that allow low-regularity (possibly discontinuous) solutions becomes the critical center-piece. In this talk I will present basic nonlocal formulations for elasticity, diffusion, conservation laws, as well as some geometric aspects for studying curvature for boundaries that lack (classical) C^2 regularity. 

A central theme will be the role of heterogeneity and boundary interactions, modeled through spatially varying operators and nonlocal boundary conditions. For these systems, I will discuss recent analytical results (including in the nonlinear regime) obtained with students and collaborators.

Particular emphasis will be placed on the limiting behavior of heterogeneous nonlocal systems as the interaction horizon tends to zero. In this regime, we identify the corresponding local (differential) models, clarify their physical interpretation, and highlight open problems and future directions motivated by

applications in continuum mechanics, biology, image processing, and beyond.