Eindhoven University of Technology (TU/e)

I have had my results for a long time: But I do not yet know how I am to arrive at them

*Carl Friedrich Gauss (1777—1855, German mathematician and physicist)*

Here, you find information on research activities, publications, and members within the Vidi project:

Funded by Dutch Research Council

Evolution equations in spaces of measures describe a wide variety of natural phenomena. The theory for such evolutions has seen tremendous growth in the last decades, which resulted in (1) the metric space theory for gradient flows, and (2) the theory of rate-independent systems for analyzing variational evolutions—evolutions driven by one or more energies/entropies. While these theories have allowed for massive development of variational evolutions in a certain direction—gradient flows with homogeneous dissipation—physics and large-deviation theory suggest the study of ** generalized gradient flows**—gradient flows with non-homogeneous dissipation—which are not covered in either theories.

In this project, we develop a theory of **dynamical-variational transport costs (DVTs)**, a class of large-deviation-inspired functionals that provide a variational generalization of a zoo of existing transport distances. DVTs generate non-homogeneous generalizations of length spaces that will be used to extend metric-space techniques to general length spaces, thereby allowing a variational framework for (A) generalized gradient flows to be rigorously investigated, and (B) the multiscale analysis of such evolutions used in the development of numerical schemes.

- Anastasiia Hraivoronska, André Schlichting and Oliver Tse. Variational convergence of the Scharfetter-Gummel scheme to the aggregation-diffusion equation and vanishing diffusion limit (arXiv:2306.02226)
- Alberto Montefusco, Upanshu Sharma and Oliver Tse. Fourier-Cattaneo equation: stochastic origin, variational formulation, and asymptotic limits (arXiv:2211.07265)
- with Anastasiia Hraivoronska. Diffusive limit of random walks on tessellations via generalized gradient flows

SIAM Journal on Mathematical Analysis, 2023. (arXiv:2202.06024) - Jasper Hoeksema and Oliver Tse. Generalized gradient structures for measure-valued population dynamics and their large-population limit

Calculus of Variations and Partial Differential Equations, 2023. (arXiv:2207.00853) - Simone Fagioli and Oliver Tse. On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility

Nonlinear Analysis, 2022. (arXiv:2105.11389) - Mark A. Peletier, Riccarda Rossi, Giuseppe Savaré and Oliver Tse. Jump processes as Generalized Gradient Flows

Calculus of Variations and Partial Differential Equations, 2022. (arXiv:2006.10624) - Bastian Hilder, Mark A. Peletier, Upanshu Sharma and Oliver Tse. An inequality connecting entropy distance, Fisher Information and large deviations

Stochastic Processes and their Applications, 2019. (arXiv:1812.04358)

- Simone Fagioli, University of L'Aquila
- Bastian Hilder, University of Stuttgart
- Jasper Hoeksema, Eindhoven University of Technology
- Anastasiia Hraivoronska, Eindhoven University of Technology
- Alberto Montefusco, Zuse Institute Berlin
- Mark A. Peletier, Eindhoven University of Technology
- Riccarda Rossi, University of Brescia
- Giuseppe Savaré, Bocconi University
- André Schlichting, University of Münster
- Upanshu Sharma, Freie Universität Berlin