4 citations · 6 across the 7 of their papers we have counts for
14 papers · 1 filter
Inverse medium scattering for a nonlinear Helmholtz equation
Roland Griesmaier, Marvin Knöller, Rainer Mandel
We discuss a time-harmonic inverse scattering problem for a nonlinear Helmholtz equation with compactly supported inhomogeneous scattering objects that are described by a nonlinear…
Ground states for Maxwell's equations in nonlocal nonlinear media
Rainer Mandel
In this paper we investigate the existence of ground states and dual ground states for Maxwell's Equations in in nonlocal nonlinear metamaterials. We prove that seve…
A uniqueness result for the Sine-Gordon breather
Rainer Mandel
In this note we prove that the sine-Gordon breather is the only quasimonochromatic breather in the context of nonlinear wave equations in .
Dual variational methods for a nonlinear Helmholtz equation with sign-changing nonlinearity
Rainer Mandel, Dominic Scheider, Tolga Yesil
We prove new existence results for a Nonlinear Helmholtz equation with sign-changing nonlinearity of the form $$ - Δu - k^{2}u = Q(x)|u|^{p-2}u, \quad u \in W^{2,p}(\mathbb{R}^{N})…
An annulus multiplier and applications to the Limiting absorption principle for Helmholtz equations with a step potential
Rainer Mandel, Dominic Scheider
We consider the Helmholtz equation on where the potential is constant on each of the half-spaces $\mathbb{R}^…
Dispersive estimates, blow-up and failure of Strichartz estimates for the Schrödinger equation with slowly decaying initial data
Rainer Mandel
The initial value problem for the homogeneous Schrödinger equation is investigated for radially symmetric initial data with slow decay rates and not too wild oscillations. Our glob…