Prof. Dr. Harald Garcke

Chair of Mathematics VIII

Department of Mathematics
University of Regensburg
93040 Regensburg
Germany
Room: M 111
Phone: +49 (0)941 943 2992
Fax: +49 (0)941 943 3263
harald.garcke@mathematik.uni-regensburg.de

Consultation-hour: Wednesday from 10:30 to 11:30 o'clock

PhD job offers in the Research Training Group IntComSin (GRK 2339)

Preprint of the article "Wie Mathematische Modelle helfen das Wachstum von Tumoren zu verstehen"

New Book:
Interfaces: modeling, analysis, numerics
by Eberhard Bänsch, Klaus Deckelnick, Harald Garcke and Paola Pozzi
(for a preprint version of the book please contact harald.garcke@ur.de)

Publications

Recent SURVEY ARTICLES
John W. Barrett, Harald Garcke, Robert Nürnberg, Parametric finite element approximations of curvature driven interface evolutions, appeared in Handbook of Numerical Analysis 21, 275-423 (2020)

Helmut Abels and Harald Garcke, Weak solutions and diffuse interface models for incompressible two-phase flows, appeared in Y. Giga, A. Novotny (eds.), Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, DOI 10.1007/978-3-319-10151-4_29-1
PREPRINT

Harald Garcke, Curvature Driven Interface Evolution, Jahresbericht der Deutschen Mathematiker-Vereinigung, September 2013, Volume 115, Issue 2, pp 63-100. DOI 10.1365/s13291-013-0066-2
For a preprint of an earlier version see PREPRINT

Mathematische Modellierung
Christof Eck, Harald Garcke, Peter Knabner
Date of publication: March 2008
2nd revised edition: March 2011
3rd revised edition: March 2017
Mathematical Modeling
Date of publication: May 2017

Interfaces: Modeling, Analysis, Numerics
Eberhard Bünsch , Klaus Deckelnick , Harald Garcke , Paola Pozzi
Date of publication: October 2023

Research

Fluidic Membranes

Numerical computations of the dynamics of fluidic membranes and vesicles, Phys. Rev. E 92, 052704 (2015) (with John W. Barrett and Robert Nürnberg)
VIDEO
Finite element approximation for the dynamics of asymmetric fluidic biomembranes, Mathematics of Computation (2016), http://dx.doi.org/10.1090/mcom/31622015 (with John W. Barrett and Robert Nürnberg)
VIDEO
A stable numerical method for the dynamics of fluidic membranes, Numerische Mathematik 134 (4), 783-822 (2016), DOI 10.1007/s00211-015-0787-5 (with John W. Barrett and Robert Nürnberg)

Mathematics of snow crystal growth

Numerical computations of facetted pattern formation in snow crystal growth, Physical Review E 86 (1) (2012), 011604 (with John W. Barrett and Robert Nürnberg)
Finite Element Approximation of One-Sided Stefan Problems with Anisotropic, Approximately Crystalline, Gibbs-Thomson Law. Adv. Differential Equations 18 (2013), 383-432 (with John W. Barrett and Robert Nürnberg)
Preprint 1 Preprint 2
VIDEO1 VIDEO2
Existence of weak solutions for the Stefan problem with anisotropic Gibbs-Thomson law
Adv. Math. Sci. Appl. 21 (2011), 255-283 (with Stefan Schaubeck)

Image Segmentation

Segmentation and restoration of images on surfaces by parametric active contours with topology changes, Journal of Mathematical Imaging and Vision 55 (1), 105-124 (2016), doi: 10.1007/s10851-015-0616-6 (with Heike Benninghoff)
WEBSITE
Segmentation of three-dimensional images with parametric active surfaces and topology changes 2015 (with Heike Benninghoff)
Image segmentation and restoration using parametric contours with free endpoints. IEEE Trans. Image Process 25 (4), 1639-1648 (2016) (with Heike Benninghoff)
PREPRINT

Shape Optimization

Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow
ESAIM-COCV, 2015, DOI: http://dx.doi.org/10.1051/cocv/2015006 (with Claudia Hecht)
PREPRINT
Relating phase field and sharp interface approaches to structural topology optimization
ESAIM: Control, Optimisation and Calculus of Variations 20 (4)(2014), 1025-1058 (with Luise Blank, M. Hassan Farshbaf-Shaker and Vanessa Styles)
PREPRINT

Phase field modelling of solidification phenomena

A diffuse interface model for alloys with multiple components and phases, SIAM J. Appl. Math. 64 (3) (2004), 775-799 (with B. Nestler and B. Stinner).
Stable phase field approximations of anisotropic solidification
2012 (with John W. Barrett and Robert Nürnberg) IMA J. Numer. Anal. 34 (4) (2014), 1289-1327. doi: 10.1093/imanum/drt044
PREPRINT

Geometric evolution equations

Local well-posedness for volume-preserving mean curvature and Willmore flows with line tension, Math. Nachr. 289 (2-3), 136-174 (2016), DOI 10.1002/mana.201400102 (with Helmut Abels and Lars Müller)
Standard planar double bubbles are stable under surface diffusion flow
(with Helmut Abels and Nasrin Arab)
Mean curvature flow with triple junctions in higher space dimensions
Archive for Rational Mechanics and Analysis 211, Issue 1 (2014), 301-334 (with Daniel Depner and Yoshihito Kohsaka)

Tumor growth

A Cahn-Hilliard-Darcy model for tumour growth with chemotaxis and active transport, Math. Models Methods Appl. Sci. 26 (6), 1095-1148 (2016) (with Kei Fong Lam, Emanuel Sitka and Vanessa Styles)

Phase separation and elastic effects

On mathematical models for phase separation in elastically stressed solids, University Bonn, 2000 (accepted).
On Cahn-Hilliard systems with elasticity, Proc. Roy. Soc. Edinburgh , 133 A, 307-331, (2003)

Geförderte Projekte der DFG

Project Diffuse interface models for transport processes at fluidic interfaces as part of the
Schwerpunktprogramm Transport Processes at Fluidic Interfaces of the DFG (SPP 1506) (May 2010 - May 2016)

Project "Mathematische Modellierung und Devicesimulation für Halbleiterbauelemente" third party funded by Infineon
Project Optimization problems governed by Cahn-Hilliard equations, joint project with Luise Blank as part of the
Schwerpunktprogramm Optimierung mit partiellen Differentialgleichungen (SPP1253/1) of the DFG (SPP1253/1) (since June 2006)
Project Phasenfeldmodellierung der Erstarrung in mehrkomponentigen und mehrphasigen Legierungssystemen
as part of the Schwerpunktprogramm Phasenumwandlungen in mehrkomponentigen Schmelzen of the DFG (until November 2006)
Project Multiple scales in phase separating systems with elastic misfit
as part of the Schwerpunktprogramm Analysis, Modellbildung und Simulation von Mehrskalenproblemen of the DFG (until 2005)
Project Analysis, modelling and simulation of multi-scale, multi-phase solidification in alloy systems
as part of the Schwerpunktprogramm Analysis, Modellbildung und Simulation von Mehrskalenproblemen of the DFG (until August 2006)
RTN-Network on Nonlinear partial differential equations describing front propagation and other singular phenomena

Group

Jonas Haselböck
Raum M 117, Tel. 0941-943-2954
jonas.haselboeck"at"mathematik.uni-regensburg.de

Paul Hüttl
Raum M 114, Tel. 0941-943-2953
paul.huettl"at"mathematik.uni-regensburg.de

Dr. Patrik Knopf
Raum M 114, Tel. 0941-943-2953
patrik.knopf"at"mathematik.uni-regensburg.de

Jonas Stange doctoral student by Dr. Patrik Knopf Raum 019 B, Tel. 0941-943-5691 jonas.stange"at"mathematik.uni-regensburg.de

Dennis Trautwein
Raum M 111A, Tel. 0941-943-4492
dennis.trautwein"at"mathematik.uni-regensburg.de

Dr. Quan Zhao (Humboldt-Stipendiat)
Raum M 004A, Tel. 0941-943-3340
quan.zhao"at"mathematik.uni-regensburg.de

Conferences

Conference

15th international Conference on Free Boundary Problems (FBP 2020), September 13 - September 17, 2021, Berlin, Germany

Conference

Mathematical Models for Bio-Medical Sciences, June 20 - June 24, 2022, Como, Italy

Workshop

French-German-Italian
Laboratoire International Associé (LIA) COPDESC, November 4-7, 2019, Paris

Workshop on PDE 2019

Partial Differential Equations in Fluids and Solids, September 9-13, 2019, Berlin

International Congress

Industrial and Applied Mathematics, July 15-19, 2019, Valencia, Spanien

Summer School

Summer School on Phase field modeling, June 24-26, 2019, Hasselt University, Belgium

COPDESC-Workshop

Calculus of Variation and Nonlinear Partial Differential Equations, March 25-28, 2019, Regensburg

Workshop

Surface, Bulk, and Geometric Partial Differential Equations:Interfacial, stochastic, non-local and discrete structures, January 20-26, 2019, Oberwolfach

Workshop

Special Materials and Complex Systems--SMACS 2018, June 18-22, 2018, Gargano, Italy

89th GAMM Annual Meeting

GAMM 2018, March 19-23, 2018, Munich, Germany

Workshop

Geometric Evolution Equations,
March 5-8, 2018, Regensburg, Germany

Conference

Equadiff 2017, July 24-28, 2017, Bratislava, Slovakia

Conference

The 14th International Conference on Free Boundary Problems: Theory and Applications, July 9-14, 2017, Shanghai Jiao Tong University, Shanghai, China

Workshop

Emerging Developments in Interfaces and Free Boundaries, January 22-28, 2017, Oberwolfach

STAMM Symposium

Trends on Applications of Mathematics to Mechanics, September 5-9, 2016, Rome, Italy

GK Winter School

Geometric Evolution Equations, February 16-19, 2016, Regensburg

Workshop

Biological Membranes: Modelling, Analysis and Numerics, January 7-8, 2016, Imperial College London

Workshop on
Geometric Partial Differential Equations: Surface and Bulk Processes, Nov 29-Dec 5, 2015, Oberwolfach
Conference on
Multi-physics geometric PDE's using deformable surfaces: Analysis, Modelling, Numerics and Applications, November 4-6, 2015, University of Sussex
International Conference on Transport Processes at Fluid Interfaces, October 5 -7, 2015, TU Darmstadt
3rd Workshop of the GAMM Activity Group
Analysis of Partial Differential Equations, September 30 - October 2, 2015, University of Kassel
Jahrestagung der Deutschen Mathematiker-Vereinigung, 21.-25.09.2015, Hamburg
ARA
Workshop of the Analysis research group Regensburg and Augsburg
February 25-26, 2014, Regensburg, Germany organized together with Helmut Abels (Regensburg)
GAMM Activity Group
Workshop for the Initiation of the GAMM Activity Group "Analysis of Partial Differential Equations"
October 1-2, 2013, Regensburg, Germany organized together with Helmut Abels (Regensburg)
Free Boundary Problems: Theory and Applications
June 11-15, 2012, Frauenchiemsee, Germany
Phase Field Models in Fluid Mechanics
February 14-16, 2011, Regensburg, Germany
organized together with Helmut Abels (Regensburg) and Günther Grün (Erlangen)
Optimization problems with interfaces and free boundaries
March 23-27, 2009, Regensburg, Germany
organized together with Luise Blank (Regensburg) and Michael Hinze (Hamburg)
Conference on Free Boundary Problems and Nonlinear PDE in honor of Willi Alt's 60th birthday, Bonn, October 21st -23rd 2005.

CV

05.06.1963 born in Bremerhaven
1989 Diploma in mathematics at University of Bonn
1989-1993 Research assistant at SFB 256 “Nichtlineare partielle Differentialgleichungen”, University of Bonn
1993 Dr. rer. nat. in mathematics, University of Bonn
1993-1994 Post-doc position at Centre for Mathematical Analysis and Its Applications (University of Sussex, England) with an ESF fellowship
1994-2000 Research assistant at University of Bonn
2000 Habilitation at University of Bonn
2000-2002 Hochschuldozent at University of Bonn
2001 Offers for a professorship in Duisburg and Regensburg
since 2002 Full professor at University of Regensburg
2005-2007 Dean of the faculty of mathematics at University of Regensburg
since 2011 Vertrauensdozent of the DFG

Prof. Dr. Harald Garcke

Chair of Mathematics VIII

Department of Mathematics University of Regensburg 93040 Regensburg Germany Room: M 111 Phone: +49 (0)941 943 2992 Fax: +49 (0)941 943 3263 harald.garcke@mathematik.uni-regensburg.de

Preprint of the article "Wie Mathematische Modelle helfen das Wachstum von Tumoren zu verstehen"

New Book: Interfaces: modeling, analysis, numerics by Eberhard Bänsch, Klaus Deckelnick, Harald Garcke and Paola Pozzi (for a preprint version of the book please contact harald.garcke@ur.de)

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Conferences

Conference

Conference

Workshop

Workshop on PDE 2019

International Congress

Summer School

COPDESC-Workshop

Workshop

Workshop

89th GAMM Annual Meeting

Workshop

Conference

Conference

Workshop

STAMM Symposium

GK Winter School

Workshop

Former Conferences

Workshop on

Conference on

3rd Workshop of the GAMM Activity Group

ARA

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CV

Department of Mathematics
University of Regensburg
93040 Regensburg
Germany
Room: M 111
Phone: +49 (0)941 943 2992
Fax: +49 (0)941 943 3263
harald.garcke@mathematik.uni-regensburg.de

New Book:
Interfaces: modeling, analysis, numerics
by Eberhard Bänsch, Klaus Deckelnick, Harald Garcke and Paola Pozzi
(for a preprint version of the book please contact harald.garcke@ur.de)