51 citations · 348 across the 35 of their papers we have counts for
36 papers
Korteweg-de Vries waves in peridynamical media
Michael Herrmann, Katia Kleine
We consider a one-dimensional peridynamical medium and show the existence of solitary waves with small amplitudes and long wavelength. Our proof uses nonlinear Bochner integral ope…
Instability of hysteretic phase interfaces in a mean-field model with inhomogeneities
Michael Herrmann, Barbara Niethammer
We study a system of non-identical bistable particles that is driven by a dynamical constraint and coupled through a non-local mean-field. Assuming piecewise affine constitutive la…
Dispersive Shock Waves in Lattices: A Dimension Reduction Approach
Christopher Chong, Michael Herrmann, P. G. Kevrekidis
Dispersive shock waves (DSWs), which connect states of different amplitude via a modulated wave train, form generically in nonlinear dispersive media subjected to abrupt changes in…
Efficient Random Walks on Riemannian Manifolds
Simon Schwarz, Michael Herrmann, Anja Sturm +1
According to a version of Donsker's theorem, geodesic random walks on Riemannian manifolds converge to the respective Brownian motion. From a computational perspective, however, ev…
A uniqueness result for a simple superlinear eigenvalue problem
Michael Herrmann, Karsten Matthies
We study the eigenvalue problem for a superlinear convolution operator in the special case of bilinear constitutive laws and establish the existence and uniqueness of a one-paramet…
Nonlinear and Nonlocal Eigenvalue Problems
Michael Herrmann, Karsten Matthies
We study a class of nonlinear eigenvalue problems which involves a convolution operator as well as a superlinear nonlinearity. Our variational existence proof is based on constrain…