Together with Antonio Esposito and Georg Heinze, we study a class of nonlocal partial differential equations presenting a tensor-mobility, in space, obtained asymptotically from nonlocal dynamics on localising infinite graphs. Our strategy relies on the variational structure of both equations, being a Riemannian and Finslerian gradient flow, respectively.… Read the rest
Together with Anastasiia Hraivoronska and Oliver Tse, we explore the convergence of the Scharfetter-Gummel scheme for the aggregation-diffusion equation using a variational approach. Our investigation involves obtaining a novel gradient structure for the finite volume scheme that works consistently for any nonnegative diffusion constant, which allows us to study the discrete-to-continuum and zero-diffusion limits simultaneously.… Read the rest
The article with Antonio Esposito and Francesco Saverio Patacchini on a class of nonlocal continuity equations on graphs got published in the European Journal of Applied Mathematics. This is a follow-up work on our previous work also with Dejan Slepcev, where we introduced evolutions on graphs based on Upwind interpolation.… Read the rest
The paper with Víctor Navarro-Fernández on Error estimates for a finite volume scheme for advection-diffusion equations with rough coefficients got published at ESAIM: Mathematical Modelling and Numerical Analysis (M2AN). In the revision (also on arXiv:2201.10411), we arrived at uniform errors estimate in the diffusion constant also in the limit of vanishing diffusion.… Read the rest
Together with Martin Burger, Franca Hoffmann, Daniel Matthes and Matthias Erbar, we investigate a new dynamical optimal transport distance in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble Kalman methods for solving inverse problems.… Read the rest
Together with Katy Craig (UC Santa Barbara), Antonio Esposito (University of Oxford) and Dimitrios Giannakis (Dartmouth College), we invite for contributions to the special issue Evolution Equations on Graphs: Analysis and Applications at European Journal of Applied Mathematics.… Read the rest
We open the call to register and contribute talks/posters at the workshop
“In search of model structures for non-equilibrium systems”,
which will take place at the University of Münster, April 2023 – 28. April 2023.
Details: https://uni-muenster.de/MathematicsMuenster/go/non-equilibrium-systems
Please register using the link (the deadline for participation is March 27):
https://wwuindico.uni-muenster.de/event/1669/registrations/
The workshop proposal together with Pierre Monmarché, Julien Reygner and Marielle Simon on PDE & Probability in interaction: functional inequalities, optimal transport and particle systems got accepted. I’m happy to see you as speaker and participant from 22-26 January 2024 at CIRM.… Read the rest
The paper with Víctor Navarro-Fernández and Christian Seis on Optimal stability estimates and a new uniqueness result for advection-diffusion equations got published at Pure and Applied Analysis.
\(\newcommand{\R}{\mathbb{R}}\)
[stextbox id=”Theorem” caption=”Navier-Stokes equation in \(d=2,3\)”]
\[ \begin{aligned}
u &: [0,\infty) \times \Omega \to \R^d &\text{velocity (unknown)} & \text{ length / time } \\
p &: [0,\infty) \times \Omega \to \R^d &\text{pressure (unknown)} & \text{ force / area } \\
f &: [0,\infty) \times \Omega \to \R^d &\text{external volume force (data)} & \text{ force / volume } \\
\varrho &\in [0,\infty) &\text{mass density (data)} & \text{ mass / volume } \\
\mu&\in (0,\infty) &\text{dynamic viscosity (data)} & \text{ pressure \(\cdot\) time }
\end{aligned}\]
\[\begin{aligned}
\varrho \left( \partial_t u + u \cdot \nabla u \right) – \mu \Delta u + \nabla p &= f &&\text{in \((0,\infty)\times \Omega\)},\\
\nabla \cdot u &= 0 &&\text{in \((0,\infty)\times \Omega\)},\\
u &= 0 &&\text{on \((0,\infty)\times \partial \Omega\)}
\end{aligned}\]
and initial conditions \(u(t=0,\cdot)=u_0(\cdot)\).… Read the rest