65 citations · 188 across the 24 of their papers we have counts for
24 papers
Curvature computations for a two-component Camassa-Holm equation with vorticity
Martin Kohlmann
In the present paper, a two-component Camassa-Holm (2CH) system with vorticity is studied as a geodesic flow on a suitable Lie group. The paper aims at presenting various details o…
Bound States for Nano-Tubes with a Dislocation
Rainer Hempel, Martin Kohlmann, Marko Stautz +1
As a model for an interface in solid state physics, we consider two real-valued potentials and on the cylinder or tube $S=\mathbb R \times (\mathbb R/\mathbb Z)…
The abstract quasilinear Cauchy problem for a MEMS model with two free boundaries
Martin Kohlmann
In this paper, we reformulate a mathematical model for the dynamics of an idealized electrostatically actuated MEMS device with two elastic membranes as an initial value problem fo…
On an elliptic-parabolic MEMS model with two free boundaries
Martin Kohlmann
We discuss an evolution free boundary problem of mixed type with two free boundaries modeling an idealized electrostatically actuated MEMS device. While the electric potential is t…
A new model for electrostatic MEMS with two free boundaries
Martin Kohlmann
A moving boundary problem with two free boundaries modeling a two-dimensional idealized MEMS device with pull-in instability is discussed. We use a fixed point argument to show tha…
The two-component Camassa-Holm system in weighted spaces
Martin Kohlmann
We present some new persistence results for the non-periodic two-component Camassa-Holm (2CH) system in weighted spaces. Working with moderate weight functions that are commo…
A note on multi-dimensional Camassa-Holm type systems on the torus
Martin Kohlmann
We present a -component nonlinear evolutionary PDE which includes the -dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as well as their partially aver…
The periodic two-dimensional --equation as an EPDiff equation
Martin Kohlmann
We introduce a periodic two-dimensional --equation and a periodic two-dimensional two-component -Camassa-Holm equation which we study as geodesic flows on the diffeomorp…
The two-dimensional periodic -equation on the diffeomorphism group of the torus
Martin Kohlmann
In this paper, the two-dimensional periodic -equation is discussed under geometric aspects, i.e., as a geodesic flow on the diffeomorphism group of the torus $\T=S^1\times S^1$.…
The Burgers equation and the Korteweg-de Vries equation with quadratic nonlinearity
Martin Kohlmann
We study generalized variants of the Burgers equation and the KdV equation on the circle. The main goal of the paper is to show that both extensions can be recast as geodesic equat…
Necrotic tumor growth: an analytic approach
Martin Kohlmann
The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine t…
Analysis of a mathematical model for the growth of cancer cells
Martin Kohlmann
In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is…
A note on a multi-layer tumor growth model
Martin Kohlmann
A two-dimensional free boundary model for the growth of multi-layer tumors has been proposed in [S. Cui, J. Escher: ARMA 191 (2009) 173-193] where the authors derive well-posedness…
Well-posedness and blow-up for a two-component Degasperis-Procesi equation with infinitely fast propagating solutions
Martin Kohlmann
In this paper, a two-component variant of the Degasperis-Procesi equation on the real line is discussed. Applying Kato's theory, we first prove the local well-posedness for the equ…
On initial boundary value problems for variants of the Hunter-Saxton equation
Martin Kohlmann
The Hunter-Saxton equation serves as a mathematical model for orientation waves in a nematic liquid crystal. The present paper discusses a modified variant of this equation, coming…
On a two-component -Camassa--Holm system
Martin Kohlmann
A novel -Camassa--Holm system is studied as a geodesic flow on a semidirect product obtained from the diffeomorphism group of the circle. We present the corresponding details of…
Dislocation problems for periodic Schrödinger operators and mathematical aspects of small angle grain boundaries
Rainer Hempel, Martin Kohlmann
We discuss two types of defects in two-dimensional lattices, namely (1) translational dislocations and (2) defects produced by a rotation of the lattice in a half-space. For Lipsch…
The curvature of semidirect product groups associated with two-component Hunter-Saxton systems
Martin Kohlmann
In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its -variant. Considering both equations as a geodesic flow on the semidirect product o…
Global existence and blow-up for a weakly dissipative DP equation
Martin Kohlmann
In this paper, we study a weakly dissipative variant of the periodic Degasperis-Procesi equation. We show the local well-posedness of the associated Cauchy problem in , $s>…
The periodic --equation and Euler equations on the circle
Martin Kohlmann
In this paper, we study the -variant of the periodic -equation and show that this equation can be realized as a metric Euler equation on the Lie group $\Diff^{\infty}(§)$ if…
Spectral Properties of Grain Boundaries at Small Angles of Rotation
Rainer Hempel, Martin Kohlmann
We study some spectral properties of a simple two-dimensional model for small angle defects in crystals and alloys. Starting from a periodic potential , we le…
A variational approach to dislocation problems for periodic Schrödinger operators
Rainer Hempel, Martin Kohlmann
As a simple model for lattice defects like grain boundaries in solid state physics we consider potentials which are obtained from a periodic potential on with p…
The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations
Joachim Escher, Martin Kohlmann, Jonatan Lenells
We use geometric methods to study two natural two-component generalizations of the periodic Camassa-Holm and Degasperis-Procesi equations. We show that these generalizations can be…
Geometric aspects of the periodic -Degasperis-Procesi equation
Joachim Escher, Martin Kohlmann, Boris Kolev
We consider the periodic $\muDP$ equation (a modified version of the Degasperis-Procesi equation) as the geodesic flow of a right-invariant affine connection on the Fréche…