Prof. Dr. Christiane Kraus

Lehrgebiete

Ingenieurmathematik, Analysis, Lineare Algebra, Variationsmethoden, Partielle Differentialgleichungen, Funktionalanalysis, Thermodynamik

Publications

Monographs

Phase Separation Coupled with Damage Processes: Analysis of Phase Field Models in Elastic Media (with Ch. Heinemann), Springer Fachmedien, Wiesbaden, 2014, 173  pages, (Monograph Published).

Articles in Refereed Journal

• Maximal convergence theorems for functions of squared modulus holomorphic type in two dimensons and some applications, J. Approx. Theory, 147, pp. 47--66, 2007.

• The equilibria of liquid-vapour systems revisited (mit W. Dreyer),  WIAS-Preprint 1238,  Berlin, 2007.

• Multivariate Polynomial Approximation of Powers of the Euclidean Distance,  Constr. Approx.,  27, pp. 323--327, 2008.

• An anisotropic, inhomogeneous, elastically modified Gibbs-Thomson law as singular limit of a diffuse interface model  (mit H. Garcke), PAMM, 10, pp. 519--520, 2010.

• On the van der Waals-Cahn-Hilliard phase-field model and its equilibria conditions in the sharp interface limit (mit W. Dreyer), Proc. Roy. Soc.  Edinburgh, 140 A, pp. 1--26, 2010.

• An anisotropic, inhomogeneous, elastically modified Gibbs-Thomson law as singular limit of a diffuse interface model  (mit H. Garcke),  Adv. Math. Sci. Appl., 20, pp. 511--545, 2010.

• Interface conditions for limits of the Navier-Stokes-Korteweg model (mit K. Hermsdoerfer und  D. Kroener), Interfaces Free Bound., 13, pp. 239--254, 2011.

• An anisotropic, inhomogeneous, elastically modified Gibbs-Thomson law as singular limit of a diffuse interface model  (mit H. Garcke), Adv. Math. Sci. Appl. , 20, pp. 511--545, 2010.

• Bernstein-Walsh type theorems for real analytic functions in several dimensions, Constr.  Approx. , 33, pp. 191--217, 2011.
  

• Existence of weak solutions for Cahn-Hilliard systems coupled with elasticity and damage (mit C. Heinemann), Adv. Math. Sci. Appl., 21, pp. 321--359, 2011.

• The degenerate and non-degenerate Stefan problem with spatially inhomogeneous and anisotropic Gibbs-Thomson law,  European J. Appl. Math., 22, pp. 393--422, 2011.
  

• Asymptotic analysis for Korteweg models (mit W. Dreyer, J. Giesselmann und C. Rohde), Interfaces Free Bound., 14, pp. 105--143, 2012.

• A diffuse interface model for quasi-incompressible flows: Sharp interface limits and numerics (mit G. Aki, J. Daube, W. Dreyer, J. Giesselmann, M. Kraenkel), ESAIM Proceedings, 38, pp. 54--77, 2012.

• Existence results for diffuse interface models describing phase separation and damage (mit C. Heinemann), European J. Appl. Math., 24, pp. 179--211, 2013.

• A quasi-incompressible diffuse model with phase transition -- modeling and sharp interface limits (mit G. Aki, W. Dreyer, J. Giesselmann), Math. Models Methods Appl. Sci., 24, pp. 827--86, 2014.

• A compressible mixture model with phase transition (mit W. Dreyer, J. Giesselmann), Phys. D, 273-274, pp. 1--13, 2014.

• Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes (mit C. Heinemann), Mathematica Bohemica, 139, pp. 315-331, 2014.

• A degenerating Cahn-Hilliard system coupled with complete damage processes (mit C. Heinemann), Nonlinear Anal. Real World Appl., 22, pp. 388--403, 2015.
  

• Modelling and analysis of a phase-field system for damage and phase separation processes in solids (mit E. Bonetti, C. Heinemann, A. Segatti), J. of Diff. Equations., 258, pp. 3928--3959, 2015

• Existence of weak solutions for a PDE system describing phase separation and  damage processes including inertia effects (mit C. Heinemann), Discrete Contin. Dyn. Syst., 35, pp. 2565--2590, 2015.

• Complete damage in linear elastic materials -- modeling, weak formulation and existence results  (mit C. Heinemann), Calc. Var. Partial Differ. Equ., 54, pp. 217--255, 2015.

• Existence of weak solutions for a hyperbolic-parabolic phase-field system with mixed boundary conditions on non-smooth domains (mit C. Heinemann), SIAM J. Math. Anal., 47, pp. 2044--2073, 2015.

• Modeling and simulation of non-isothermal rate-dependent damage processes in inhomogeneous materials using the phase-field approach (mit M. Radszuweit), Computational Mechanics, 60, pp. 163--179, 2017.

• Existence of weak solutions for the Cahn--Hilliard reaction model including elastic effects and damage (mit A. Roggensack),  J. Partial Differ. Equ., 30, pp. 111-145, 2017.

• A temperature-dependent phase-field model for phase separation and damage (mit C. Heinemann, E. Rocca und R. Rossi), Arch. Ration. Mech.  Anal. , 225, pp. 177--247, 2017.
• The Sharp-Interface Limit for the Navier-Stokes-Korteweg Equations (mit H. Abels, J. Daube,  Dietmar Kröner), in "Theory, Numerics and Applications of Hyperbolic Problems I", pp. 1-13, 2018.
  

• Pressure Reconstruction for the Two-Phase Incompressible Navier-Stokes Equations (mit H. Abels, J. Daube), Asymptotic Analysis, 113, pp.  51–86, 2019.
                                              
  

Contributions to Collected Editions

• C3 -- Phase transformation and separation in solids  (with D. Knees, R. Kornhuber, A. Mielke, J. Sprekels), in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 189--203.

•  Sharp interface limit of a diffuse interface model of Navier--Stokes--Allen--Cahn type for mixtures, in: Hyperbolic Techniques for Phase Dynamics, Workshop, June 9--15, 2013, 29 of Oberwolfach Reports, Mathematisches Forschungsinstitut Oberwolfach, 2013, pp. 1719--1722.

• Damage processes coupled with phase separation in elastically stressed alloys  (with Ch. Heinemann), in: Proceedings in Applied Mathematics and Mechanics (PAMM), 12, 2012, pp. 153--154.

• An inhomogeneous, anisotropic, elastically modified Gibbs-Thomson law as singular limit of a diffuse interface model (with H. Garcke) , 10 of Proceedings in Applied Mathematics and Mechanics (PAMM), 2010, pp. 519--520.
  

Diploma thesis

Numerische Approximation konformer Abbildungen durch Polynome

PhD thesis

On some Maximal Convergence Theorems for Real Analytic Functions in several dimensons