64 citations · 370 across the 28 of their papers we have counts for
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Entropic and gradient flow formulations for nonlinear diffusion
Nicolas Dirr, Marios Stamatakis, Johannes Zimmer
Nonlinear diffusion is considered for a class of nonlinearities . It is shown that for suitable choices of , an associated Lyapunov functional can be…
Travelling waves for a Frenkel-Kontorova chain
Boris Buffoni, Hartmut Schwetlick, Johannes Zimmer
In this article, the Frenkel-Kontorova model for dislocation dynamics is considered, where the on-site potential consists of quadratic wells joined by small arcs, which can be spin…
Entropy production and the geometry of dissipative evolution equations
Celia Reina, Johannes Zimmer
Purely dissipative evolution equations are often cast as gradient flow structures, , where the variable of interest evolv…
A convergent string method: Existence and approximation for the Hamiltonian boundary-value problem
Hartmut Schwetlick, Johannes Zimmer
This article studies the existence of long-time solutions to the Hamiltonian boundary value problem, and their consistent numerical approximation. Such a boundary value problem is,…