25 citations · 48 across the 8 of their papers we have counts for
11 papers
Discrete approximation of the minimizing movement scheme for evolution equations of Wasserstein gradient flow type with nonlinear mobility
Jonathan Zinsl, Daniel Matthes
We propose a fully discrete variational scheme for nonlinear evolution equations with gradient flow structure on the space of finite Radon measures on an interval with respect to a…
Existence of solutions for a class of fourth order cross-diffusion systems of gradient flow type
Daniel Matthes, Jonathan Zinsl
This article is concerned with the existence and the long time behavior of weak solutions to certain coupled systems of fourth-order degenerate parabolic equations of gradient flow…
Well-posedness of evolution equations with time-dependent nonlinear mobility: a modified minimizing movement scheme
Jonathan Zinsl
We prove the existence of nonnegative weak solutions to a class of second and fourth order nonautonomous nonlinear evolution equations with an explicitly time-dependent mobility fu…
The gradient flow of a generalized Fisher information functional with respect to modified Wasserstein distances
Jonathan Zinsl
This article is concerned with the existence of nonnegative weak solutions to a particular fourth-order partial differential equation: it is a formal gradient flow with respect to…
High-frequency limit of non-autonomous gradient flows
Simon Plazotta, Jonathan Zinsl
We study the high-frequency limit of non-autonomous gradient flows in metric spaces of energy functionals comprising an explicitly time-dependent perturbation term which might osci…
Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structure
Daniel Loibl, Daniel Matthes, Jonathan Zinsl
We prove the global-in-time existence of nonnegative weak solutions to a class of fourth order partial differential equations on a convex bounded domain in arbitrary spatial dimens…
Exponential convergence to equilibrium in a Poisson-Nernst-Planck-type system with nonlinear diffusion
Jonathan Zinsl
We investigate a Poisson-Nernst-Planck type system in three spatial dimensions where the strength of the electric drift depends on a possibly small parameter and the particles are…
A note on the variational analysis of the parabolic-parabolic Keller-Segel system in one spatial dimension
Jonathan Zinsl
We prove the existence of global-in-time weak solutions to a version of the parabolic-parabolic Keller-Segel system in one spatial dimension. If the coupling of the system is suita…
Geodesically convex energies and confinement of solutions for a multi-component system of nonlocal interaction equations
Jonathan Zinsl
We consider a system of nonlocal interaction evolution equations on with a differentiable matrix-valued interaction potential . Under suitable conditions on c…
Transport distances and geodesic convexity for systems of degenerate diffusion equations
Jonathan Zinsl, Daniel Matthes
We introduce Wasserstein-like dynamical transport distances between vector-valued densities on the real line. The mobility function from the scalar theory is replaced by a mobility…
Exponential convergence to equilibrium in a coupled gradient flow system modelling chemotaxis
Jonathan Zinsl, Daniel Matthes
We study a system of two coupled nonlinear parabolic equations. It constitutes a variant of the Keller-Segel model for chemotaxis, i.e. it models the behaviour of a population of b…