Martin Lazar

Visiting Scientist (August 15th, 2021 – June 30th, 2022 || September 12nd – September 23th, 2022)

Funded by AvH -Alexander von Humboldt Stiftung/Foundation

University of Dubrovnik

My research area covers several topics ranging from microanalysis via applied mathematics to geophysical fluid dynamics.

Currently, I focus mainly on control theory and, in particular, on parameter dependent problems. The research topics include: Control theory: Control of parameter dependent systems (greedy control, averaged control), optimal control of parabolic problems Microlocal analysis: PDEs and homogenisation, velocity averaging, microlocal defect functionals (1-scale H-measures, semiclassical measures, H-distributions) Geophysical fluid dynamics: analytical modelling in oceanography.

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Approximating the 1D wave equation using Physics Informed Neural Networks (PINNs) Code: • See the complete report by Dania Sana   Introduction Accurate and fast predictions of numerical solutions are of significant interest in many areas of science and industry. On one hand, most theoretical methods […]
Derivation of the pressure function Code: Files to run: nocircle.m, onecircle.m or twocircles.m   1 Introduction This post presents the results of my Bachelor thesis about the modeling and implementation of gas networks at stationary states. Using the isothermal Euler equations to describe the gas flow […]
Author: Daniël Veldman, FAU DCN-AvH Code: A sheep herding game in MATLAB developed for the Long Night of Science #NdW22 (Lange Nacht der Wissenschaft) Erlangen-Furth-Nuernberg 2022. Main rules • The dog should drive sheep to the target (red). • You can steer the dog with the […]
Author: Martín Hernández, FAU DCN-AvH Code: In this repository, we show a code for Lloyd’s algorithm. Also called Voronoid iteration, this is an iterative algorithm finding for equispaced convex cells in euclidean space. Lloyd’s algorithm finds the distribution of the cells computing their center of mass […]
Using the support function for optimal shape design   1 Motivation Led by problems of optimal placement and design of sensors, we are interested in considering the following shape optimization problem where is the Hausdorff distance between and defined as follows with is the distance from […]
Uniform Turnpike Property 1 Introduction In this post, we analyze a heat equation with rapidly oscillating coefficients dependent on a parameter , with a distributed control. We show that the uniform null controllability implies the uniform turnpike property, i.e., the turnpike property with constants independent of […]
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