31 citations · 32 across the 10 of their papers we have counts for
15 papers
A Hydrodynamics Formulation for a Nonlinear Dirac Equation
Joan Morrill i Gavarró, Michael Westdickenberg
We derive a hydrodynamics formulation for a modified Dirac equation with a nonlinear mass term that preserves the homogeneity of the original Dirac equation. The nonlinear Dirac eq…
Avoidance of non-strict saddle points by blow-up
El Mehdi Achour, Umberto L. Hryniewicz, Michael Westdickenberg
It is an old idea to use gradient flows or time-discretized variants thereof as methods for solving minimization problems. In some applications, for example in machine learning con…
Sharp Convergence to the Half-Space for Mullins-Sekerka in the Plane
Wenhui Shi, Maria G. Westdickenberg, Michael Westdickenberg
We revisit the HED Method for the Mullins-Sekerka evolution in the plane. We identify a natural notion of distance, intrinsic to the interface itself. Using this distance, the ener…
Minimal acceleration for the multi-dimensional isentropic Euler equations
Michael Westdickenberg
On the set of dissipative solutions to the multi-dimensional isentropic Euler equations we introduce a quasi-order by comparing the acceleration at all times. This quasi-order is c…
New Coupling Conditions for Isentropic Flow on Networks
Yannick Holle, Michael Herty, Michael Westdickenberg
We introduce new coupling conditions for isentropic flow on networks based on an artificial density at the junction. The new coupling conditions can be derived from a kinetic model…
Flow Solutions of Transport Equations
Sholeh Karimghasemi, Siegfried Müller, Michael Westdickenberg
Under general assumptions on the velocity field, it is possible to construct a flow that is forward untangled. Once such a flow has been selected, the associated transport problem…
Learning deep linear neural networks: Riemannian gradient flows and convergence to global minimizers
Bubacarr Bah, Holger Rauhut, Ulrich Terstiege +1
We study the convergence of gradient flows related to learning deep linear neural networks (where the activation function is the identity map) from data. In this case, the composit…
One-dimensional granular system with memory effects
Charlotte Perrin, Michael Westdickenberg
We consider a hybrid compressible/incompressible system with memory effects introduced by Lefebvre Lepot and Maury (2011) for the description of one-dimensional granular flows. We…
Convergence of approximate solutions of conservation laws
Sebastian Noelle, Michael Westdickenberg
In this paper we consider convergence of approximate solutions of conservation laws. We start with an overview over the historical developments since the 1950s, and the analytical…
Characterization of the tangent space of monotone transport plans in with prescribed first projection
Marc Sedjro, Michael Westdickenberg
We provide a complete description of the tangent space of the cone of monotone plans in with prescribed first projection. We show that elements of this tangent space…
A variational time discretization for the compressible Euler equations
Fabio Cavalletti, Marc Sedjro, Michael Westdickenberg
We introduce a variational time discretization for the multi-dimensional gas dynamics equations, in the spirit of minimizing movements for curves of maximal slope. Each timestep re…
A Simple Proof of Global Existence for the 1D Pressureless Gas Dynamics Equations
Fabio Cavalletti, Marc Sedjro, Michael Westdickenberg
Sticky particle solutions to the one-dimensional pressureless gas dynamics equations can be constructed by a suitable metric projection onto the cone of monotone maps, as was shown…
The Polar Cone of the set of monotone maps
Fabio Cavalletti, Michael Westdickenberg
We prove that every element of the polar cone to the closed convex cone of monotone transport maps can be represented as the divergence of a measure field taking values in the posi…
Finite energy solutions to the isentropic Euler equations with geometric effects
Philippe G. LeFloch, Michael Westdickenberg
Considering the isentropic Euler equations of compressible fluid dynamics with geometric effects included, we establish the existence of entropy solutions for a large class of init…
Variational Particle Schemes for the Porous Medium Equation and for the System of Isentropic Euler Equations
Michael Westdickenberg, Jon Wilkening
Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework o…