65 citations · 188 across the 24 of their papers we have counts for
11 papers · 1 filter
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…