Zobrazeno 1 - 10
of 162
pro vyhledávání: '"Pietschmann, Jan"'
We study a nonlocal Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects and degenerate mobility. The nonlocality is described by means of a symmetric singular kernel. We define a notion of weak solution adapted to possible d
Externí odkaz:
http://arxiv.org/abs/2408.07396
We study the existence of weak solutions for a model of cell invasion into the extracellular matrix (ECM), which consists of a non-linear partial differential equation for the density of cells, coupled with an ordinary differential equation (ODE) des
Externí odkaz:
http://arxiv.org/abs/2407.11228
This paper models gas networks as metric graphs, with isothermal Euler equations at the edges, Kirchhoff's law at interior vertices and time-(in)dependent boundary conditions at boundary vertices. For this setup, a generalized $p$-Wasserstein metric
Externí odkaz:
http://arxiv.org/abs/2405.01698
We study some properties of a multi-species degenerate Ginzburg-Landau energy and its relation to a cross-diffusion Cahn-Hilliard system. The model is motivated by multicomponent mixtures where crossdiffusion effects between the different species are
Externí odkaz:
http://arxiv.org/abs/2307.05985
In this note we continue the study of nonlocal interaction dynamics on a sequence of infinite graphs, extending the results of [Esposito et. al 2023+] to an arbitrary number of species. Our analysis relies on the observation that the graph dynamics f
Externí odkaz:
http://arxiv.org/abs/2306.17414
Autor:
Amadori, Debora, Andreianov, Boris, Di Francesco, Marco, Fagioli, Simone, Girard, Théo, Goatin, Paola, Markowich, Peter, Pietschmann, Jan F., Rosini, Massimiliano D., Russo, Giovanni, Stivaletta, Graziano, Wolfram, Marie-Therese
We provide an overview of the results on Hughes' model for pedestrian movements available in the literature. After the first successful approaches to solving a regularised version of the model, researchers focused on the structure of the Riemann prob
Externí odkaz:
http://arxiv.org/abs/2305.10076
We introduce a free boundary model to example the effect of vesicle transport onto neurite growth. It consists of systems of drift-diffusion equations describing the evolution of the density of antero- and retrograde vesicles in each neurite coupled
Externí odkaz:
http://arxiv.org/abs/2302.00527
We provide a numerical realisation of an optimal control problem for pedestrian motion with agents that was analysed in Herzog, Pietschmann, Winkler: "Optimal Control of Hughes' Model for Pedestrian Flow via Local Attraction.", arXiv 2011.03580, 2020
Externí odkaz:
http://arxiv.org/abs/2301.02516
We present a framework enabling variational data assimilation for gradient flows in general metric spaces, based on the minimizing movement (or Jordan-Kinderlehrer-Otto) approximation scheme. After discussing stability properties in the most general
Externí odkaz:
http://arxiv.org/abs/2205.12172
We explore the dynamical behavior and energetic properties of a model of two species that interact nonlocally on finite graphs. The authors recently introduced the model in the context of nonquadratic Finslerian gradient flows on generalized graphs f
Externí odkaz:
http://arxiv.org/abs/2204.09553