Garcke, Harald

1. Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with\n chemotaxis
   2018/07/02 by Matthias Ebenbeck, Ebenbeck, Matthias, Harald Garcke +1 · 6 citations
   Computer Science · Materials Science · #35D30 #35K35 #35Q92 #76D07 #92C50 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Solidification and crystal growth phenomena
2. Global regularity and asymptotic stabilization for the incompressible Navier-Stokes-Cahn-Hilliard model with unmatched densities
   2022/09/22 by Helmut Abels, Abels, Helmut, Harald Garcke +2 · 7 citations
   Mathematics · Materials Science · #Navier-Stokes equation solutions #Solidification and crystal growth phenomena #Nonlinear Partial Differential Equations
3. Well-posedness of a Cahn--Hilliard system modelling tumour growth with chemotaxis and active transport
   2015/11/19 by Garcke, Harald, Lam, Kei Fong · 3 citations
   #35K50 #35K57 #35Q92 #92B05 #Analysis of PDEs (math.AP) #FOS: Biological sciences #FOS: Mathematics #Tissues and Organs (q-bio.TO)
4. Mathematical Analysis of a Diffuse Interface Model for Multi-Phase Flows of Incompressible Viscous Fluids with Different Densities
   2023/08/22 by Abels, Helmut, Garcke, Harald, Poiatti, Andrea · 4 citations
   #35B40 #35B65 #35Q30 #35Q35 #76D03 #76D05 #76D45 #Analysis of PDEs (math.AP) #FOS: Mathematics
5. A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow
   2014/02/26 by Garcke, Harald, Hinze, Michael, Kahle, Christian · 2 citations
   #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)
6. Optimal control of treatment time in a diffuse interface model of tumor\n growth
   2016/08/01 by Harald Garcke, Kei-Fong Lam, Garcke, Harald +3 · 2 citations
   Mathematics · Computer Science · Materials Science · #Mathematical Biology Tumor Growth #Advanced Mathematical Modeling in Engineering #Solidification and crystal growth phenomena
7. Diffuse interface modelling of soluble surfactants in two-phase flow
   2013/03/11 by Garcke, Harald, Lam, Kei Fong, Stinner, Björn · 1 citation
   #35C20 #35Q35 #35R01 #35R35 #76D45 #76T99 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
8. Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow
   2014/07/21 by Garcke, Harald, Hecht, Claudia · 1 citation
   #FOS: Mathematics #Optimization and Control (math.OC)
9. Shape optimization for surface functionals in Navier--Stokes flow using a phase field approach
   2015/04/24 by Garcke, Harald, Hecht, Claudia, Hinze, Michael +2 · 1 citation
   #35Q35 #35R35 #49Q10 #49Q12 #FOS: Mathematics #Optimization and Control (math.OC)
10. Global weak solutions and asymptotic limits of a Cahn--Hilliard--Darcy\n system modelling tumour growth
    2016/08/31 by Harald Garcke, Kei Fong Lam, Garcke, Harald +1 · 1 citation
    Mathematics · Materials Science · #Nonlinear Partial Differential Equations #Solidification and crystal growth phenomena
11. Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase\n Flow with Surfactants
    2017/10/09 by Helmut Abels, Harald Garcke, Abels, Helmut +3 · 1 citation
    Engineering · Mathematics · #Fluid Dynamics and Thin Films #Lattice Boltzmann Simulation Studies #Navier-Stokes equation solutions
12. On a Cahn-Hilliard-Brinkman model for tumour growth and its singular limits
    2018/11/16 by Matthias Ebenbeck, Harald Garcke, Ebenbeck, Matthias +1 · 1 citation
    Computer Science · Mathematics · #35D30 #35K35 #35Q92 #76D07 #92C50 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations
13. Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces
    2022/01/01 by Charles M. Elliott, Elliott, Charles M., Harald Garcke +3 · 2 citations
    Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA)
14. Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Local Well-Posedness
    2024/07/20 by Helmut Abels, Harald Garcke, Abels, Helmut +3 · 2 citations
    Computer Science · Engineering · #35D35 #35Q30 #35Q35 #76D05 #76T06 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Lattice Boltzmann Simulation Studies
15. Sharp interface analysis of a diffuse interface model for cell blebbing with linker dynamics
    2023/02/09 by Nöldner, Philipp, Burger, Martin, Garcke, Harald · 1 citation
    #34E05 #35K60 #92C37 #Analysis of PDEs (math.AP) #FOS: Mathematics
16. Multi-material phase field approach to structural topology optimization
    2013/12/09 by Blank, Luise, Farshbaf-Shaker, M. Hassan, Garcke, Harald +2 · 1 citation
    #49Q10 #65K15 #74P05 #74P15 #90C52 #FOS: Mathematics #Optimization and Control (math.OC)
17. Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Global Well-Posedness
    2024/08/14 by Helmut Abels, Harald Garcke, Abels, Helmut +3 · 2 citations
    Computer Science · Engineering · #35D35 #35Q30 #35Q35 #76D05 #76T06 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Heat Transfer #Fluid Dynamics and Thin Films
18. Structure-preserving parametric finite element method for curve diffusion based on Lagrange multiplier approaches
    2024/08/24 by Harald Garcke, Wei Jiang, Garcke, Harald +5 · 1 citation
    Engineering · #35K55 #53C44 #65M12 #65M60 #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
19. Convergence analysis for the Barrett--Garcke--Nurnberg method of transport type for evolving curves
    2025/09/09 by Genming Bai, Harald Garcke, Bai, Genming +3 · 2 citations
    Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
20. Diffuse Interface Models for Two-Phase Flows with Phase Transition: Modeling and Existence of Weak Solutions
    2025/05/08 by Helmut Abels, Harald Garcke, Abels, Helmut +2 · 2 citations
    Engineering · Materials Science · Mathematics · #35D35 #35Q30 #35Q35 #76D05 #76T06 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Navier-Stokes equation solutions #Solidification and crystal growth phenomena
21. The anisotropic Cahn--Hilliard equation with degenerate mobility: Existence of weak solutions
    2025/02/19 by Harald Garcke, Garcke, Harald, Patrik Knopf +3 · 1 citation
    Computer Science · Materials Science · Mathematics · #35D30 #35K55 #35K61 #74E10 #82C26 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Solidification and crystal growth phenomena