Veröffentlichungen
Artikel und Arbeiten
1.
Ein polynomiales, primal-duales Innere-Punkte-Verfahren mit endlicher Genauigkeit
zur Lösung linearer Programme
Master Thesis, Universität Augsburg, 79 pp., 1989
2.
Asymptotic Behaviour of Spherical Symmetric Solutions of Semilinear Elliptic Equations
PhD Thesis, Universität Augsburg, 91 pp., 1991
3.
Radial solutions of semilinear elliptic equations with prescribed numbers of zeros (Summary)
Proc. Equadiff 91, 716-721, 1993
4.
Infinitely many positive solutions of semilinear elliptic problems via sub- and supersolutions
Comm. Partial Differential Equations, 18 (7 & 8): 1219-1229, 1993
5.
Non-convergent radial solutions of semilinear elliptic equations
Asymptotic Anal., 8: 363-377, 1994
6.
Radial solutions of semilinear elliptic equations with prescribed numbers of zeros
J. Differential Equations, 107(1): 175-205, 1994
7.
Symmetry-breaking at non-positive solutions of semilinear elliptic equations
Arch. Rat. Mech. Anal., 126 (4): 299-331, 1994
8.
Selected Methods for Partial Differential Equations with Symmetry
Habilitationsschrift, Universität Augsburg, 217 pp., 1995
9.
Asymptotic behavior of solution continua for semilinear elliptic problems
Canad. Appl. Math. Quarterly, 4(2): 211-228, 1996
10.
Spatial dynamics of time periodic solutions for the Ginzburg-Landau equation
Z. Angew. Math. Phys., 47: 265-305, 1996
11.
A systematic study of heteroclinic cycles in dynamical systems with broken symmetries
Proc. Roy. Soc. Edinburgh, 126A: 885-909, 1996
12.
Perturbation of doubly periodic solution branches with applications to the Cahn-Hilliard equation
Phys. D, 100(3-4): 257-278, 1997
13.
Solutions of nonlinear planar elliptic problems with triangle symmetry
J. Differential Equations, 136(1): 1-34, 1997
14.
On Neumann problems for semilinear elliptic equations with critical nonlinearity: existence and symmetry of multi-peaked solutions
Comm. Partial Differential Equations, 22(9 & 10): 1493-1527, 1997
15.
Spinodal decomposition for the Cahn-Hilliard equation in higher dimensions. Part I: Probability and wavelength estimate
Comm. Math. Phys., 195: 435-464, 1998
16.
Convergence for radially symmetric solutions of quasilinear elliptic equations is generic
Math. Ann., 311: 177-197, 1998
17.
Spinodal decomposition in the linear Cahn-Hilliard model
Z. Angew. Math. Mech., 78: 1003-1004, 1998
18.
Maximality of the hypercube group
Rocky Mountain J. Math., 29: 1455-1465, 1999
19.
Spinodal decomposition for the Cahn-Hilliard equation in higher dimensions. Nonlinear Dynamics
Arch. Rat. Mech. Anal., 151: 187-219, 2000
20.
Spinodal decomposition for multi-component Cahn-Hilliard systems
J. Stat. Phys., 98: 871-896, 2000
21.
Heteroclinic cycles for reaction diffusion systems by forced symmetry-breaking
Trans. Amer. Math. Soc., 352: 2937-2991, 2000
22.
Nonlinear standing and rotating waves on the sphere
J. Differential Equations, 166: 402-442, 2000
23.
Spinodal decomposition for the stochastic Cahn-Hilliard equation
Proc. Equadiff 99, Vol. 2, 1265-1267, 2000
24.
Spinodal decomposition: A survey of recent results
Proc. Equadiff 99, Vol 2, 1288-1299, 2000
25.
Surface roughness in molecular beam epitaxy
Stochastics Dynam., 1: 239-260, 2001
26.
Losing a graph with surface diffusion
Hokkaido Mathematical Journal, 30: 297-305, 2001
27.
Spinodal decomposition for the Cahn-Hilliard-Cook equation
Comm. Math. Phys., 223: 553-582, 2001
28.
Roughness in surface growth equations
Interfaces and Free Boundaries, 3: 465-484, 2001
29.
The stochastic Landau equation as an amplitude equation
Discrete Contin. Dynam. Syst.-Series B., 1: 527-541, 2001
30.
Path-following the equilibria of the Cahn-Hilliard equation on the square
J. Comput. Visualization Sci., 5: 115-138, 2002
31.
Stochastic Navier-Stokes and renormalization group theory
Phys. D, 173: 137-152, 2002
32.
Spinodal decomposition in the presence of elastic interactions
In: Geometric Analysis and Nonlinear Partial Differential Equations, S. Hildebrandt und H. Karcher (eds.), Springer, 603-635, 2002
33.
Pattern formation below criticality forced by noise
Z. Angew. Math. Phys., 54: 1-25, 2003
34.
Spinodal decomposition for spatially discrete Cahn-Hilliard equations
DCDIS Series A: Mathematical Analysis, 12: 529-554, 2005
35.
Phase separation in stochastic Cahn-Hilliard models
In: Mathematical Methods and Models in Phase Transitions, A. Miranville (ed.), 1-44, 2005
36.
Discrete dynamics for convex and non-convex smoothing functionals in PDE based image restoration
Comm. Pure Appl. Anal., 5: 181-200, 2006
37.
Connecting continua and curves of equilibria of the Cahn-Hilliard equation on the square
Discrete and Continuous dynamical systems, 15(4): 1137-1153, 2006
38.
Structure of the attractor of the Cahn-Hilliard equation on the square
International J. Bifur. Chaos Appl. Sci. Engrg., 17(4): 1221-1263, 2007
39.
Second phase spinodal decomposition for the Cahn-Hilliard-Cook equation
Trans. Amer. Math. Soc., 360(1): 449-489, 2008
40.
Rigorous numerics for the Cahn-Hilliard equation on the unit square
Rev. Mat. Complut., 21(2): 351-426, 2008
41.
Stability analysis of two-dimensional pool-boiling systems
SIAM J. Appl. Dyn. Systems, 7(3): 933-961, 2008
42.
Computation of connection matrices using the software package conley
International J. Bifurcation Chaos Appl. Sci. Engrg., 19(9): 3033-3056, 2009
43.
Conley Index Theory
In: Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems, Budapest (Hungary), A. Edelmayer (ed.), 1645-1651, 2010
Preprints
1.
The set of equilibria for the Allen-Cahn equation on the square
Universität Augsburg, Report Nr. 420, 21 pp., 1999
2.
Rigorous numerics for partial differential equations using Conley index theory
12 pp., 2003
3.
Equilibria and attractor of the Cahn-Hilliard equation on the square
19 pp., 2005
Skripten
•
The Cahn-Hilliard Equation
Lecture Script SS 96, Universität Augsburg, 52 pp., 1996
•
Partielle Differentialgleichungen
Vorlesungsskript SS 2004, SS 2008, SS 2013, SS 2018 und SS 2022, RWTH Aachen University, 100 pp., 2022 PDF
•
Dynamische Systeme
Vorlesungsskript WS 2020/2021, RWTH Aachen University, 89 pp., 2021 PDF
•
Funktionalanalysis
Vorlesungsskript WS 2021/2022, RWTH Aachen University, 103 pp., 2022 PDF
•
Höhere Mathematik 4 für Physiker: Funktionalanalytische Grundlagen der Quantenmechanik
Vorlesungsskript SS 2016, RWTH Aachen University, 45 pp., 2016
Bücher
•
Höhere Mathematik I
Mainz-Verlag, 4.Auflage, 2018
Vgl. auch: https://verlag-mainz.de/verlag/hohere-mathematik-i-fc3bcr-elektrotechniker-und-physiker-html/
•
Höhere Mathematik II
Mainz-Verlag, 4.Auflage, 2019
Vgl. auch: https://verlag-mainz.de/verlag/hoehere-mathematik-ii/
•
Höhere Mathematik III
Mainz-Verlag, 4.Auflage, 2019
Vgl. auch: https://verlag-mainz.de/verlag/hoehere-mathematik-iii/
•
Höhere Mathematik IV
Mainz-Verlag, 1.Auflage, 2020
Vgl. auch: https://verlag-mainz.de/verlag/hoehere-mathematik-iv-fuer-elektrotechniker-und-physiker/
Weitere Arbeiten aus der Arbeitsgruppe
1.
Minimierer der eindimensionalen Ginzburg-Landau-Energie unter einer Mittelwertbedingung und Konvergenzraten der Cahn-Hilliard-Evolution
Masterarbeit, Lehrstuhl für Angewandte Analysis, RWTH Aachen, 115 pp., 2020 PDF