Garcke, Harald; Hüttl, Paul; Kahle, Christian; Knopf, Patrik Sharp-interface limit of a multi-phase spectral shape optimization problem for elastic structures. (English) Zbl 07791681 Appl. Math. Optim. 89, No. 1, Paper No. 24, 58 p. (2024). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q74 35C20 35P05 35R35 49Q10 49R05 74B05 74P05 74P15 PDFBibTeX XMLCite \textit{H. Garcke} et al., Appl. Math. Optim. 89, No. 1, Paper No. 24, 58 p. (2024; Zbl 07791681) Full Text: DOI arXiv OA License
Garcke, Harald; Hüttl, Paul; Kahle, Christian; Knopf, Patrik; Laux, Tim Phase-field methods for spectral shape and topology optimization. (English) Zbl 1512.35411 ESAIM, Control Optim. Calc. Var. 29, Paper No. 10, 57 p. (2023). Reviewer: Giuseppe Buttazzo (Pisa) MSC: 35P05 35P15 35R35 49M05 49M41 49K20 49J20 49J40 49Q10 49R05 PDFBibTeX XMLCite \textit{H. Garcke} et al., ESAIM, Control Optim. Calc. Var. 29, Paper No. 10, 57 p. (2023; Zbl 1512.35411) Full Text: DOI arXiv
Garcke, Harald; Rauchecker, Maximilian Stability analysis for stationary solutions of the Mullins-Sekerka flow with boundary contact. (English) Zbl 1523.35035 Math. Nachr. 295, No. 4, 683-705 (2022). MSC: 35B35 35B40 35Q35 35R35 53A10 PDFBibTeX XMLCite \textit{H. Garcke} and \textit{M. Rauchecker}, Math. Nachr. 295, No. 4, 683--705 (2022; Zbl 1523.35035) Full Text: DOI arXiv
Ebenbeck, Matthias; Garcke, Harald; Nürnberg, Robert Cahn-Hilliard-Brinkman systems for tumour growth. (English) Zbl 1480.35411 Discrete Contin. Dyn. Syst., Ser. S 14, No. 11, 3989-4033 (2021). MSC: 35R35 35C20 35K35 35K57 65M60 35Q92 92C42 PDFBibTeX XMLCite \textit{M. Ebenbeck} et al., Discrete Contin. Dyn. Syst., Ser. S 14, No. 11, 3989--4033 (2021; Zbl 1480.35411) Full Text: DOI arXiv
Garcke, H.; Gößwein, M. Non-linear stability of double bubbles under surface diffusion. (English) Zbl 1482.35110 J. Differ. Equations 302, 617-661 (2021). Reviewer: Dimitra Antonopoulou (Chester) MSC: 35K55 53C42 35R35 35K93 35B40 PDFBibTeX XMLCite \textit{H. Garcke} and \textit{M. Gößwein}, J. Differ. Equations 302, 617--661 (2021; Zbl 1482.35110) Full Text: DOI arXiv
Barrett, John W.; Garcke, Harald; Nürnberg, Robert Parametric finite element approximations of curvature-driven interface evolutions. (English) Zbl 1455.35185 Bonito, Andrea (ed.) et al., Geometric partial differential equations. Part I. Amsterdam: Elsevier/North Holland. Handb. Numer. Anal. 21, 275-423 (2020). MSC: 35Q35 76D05 76D07 76T06 76M10 80A22 92C05 65M60 65N30 65M22 35R35 PDFBibTeX XMLCite \textit{J. W. Barrett} et al., Handb. Numer. Anal. 21, 275--423 (2020; Zbl 1455.35185) Full Text: DOI arXiv
Garcke, H.; Gößwein, M. On the surface diffusion flow with triple junctions in higher space dimensions. (English) Zbl 1439.53079 Geom. Flows 5, 1-39 (2020). Reviewer: Rodica Luca (Iaşi) MSC: 53E10 35K52 35K93 35R35 35K55 PDFBibTeX XMLCite \textit{H. Garcke} and \textit{M. Gößwein}, Geom. Flows 5, 1--39 (2020; Zbl 1439.53079) Full Text: DOI arXiv
Elliott, Charles M. (ed.); Garcke, Harald (ed.); Kornhuber, Ralf (ed.) Surface, bulk, and geometric partial differential equations: interfacial, stochastic, non-local and discrete structures. Abstracts from the workshop held January 20–26, 2019. (English) Zbl 1439.00061 Oberwolfach Rep. 16, No. 1, 133-207 (2019). MSC: 00B05 00B25 35-06 35Q92 35R35 49Q10 65Mxx 65Nxx PDFBibTeX XMLCite \textit{C. M. Elliott} (ed.) et al., Oberwolfach Rep. 16, No. 1, 133--207 (2019; Zbl 1439.00061) Full Text: DOI
Abels, Helmut; Garcke, Harald; Weber, Josef Existence of weak solutions for a diffuse interface model for two-phase flow with surfactants. (English) Zbl 1404.35340 Commun. Pure Appl. Anal. 18, No. 1, 195-225 (2019). MSC: 35Q35 76T99 35Q30 35R35 76D05 76D45 35A01 35D30 65M06 PDFBibTeX XMLCite \textit{H. Abels} et al., Commun. Pure Appl. Anal. 18, No. 1, 195--225 (2019; Zbl 1404.35340) Full Text: DOI arXiv
Garcke, Harald; Hinze, Michael; Kahle, Christian; Lam, Kei Fong A phase field approach to shape optimization in Navier-Stokes flow with integral state constraints. (English) Zbl 1406.35274 Adv. Comput. Math. 44, No. 5, 1345-1383 (2018). MSC: 35Q35 35Q56 35R35 49Q10 49Q12 65M22 65M60 76S05 35B65 76D05 PDFBibTeX XMLCite \textit{H. Garcke} et al., Adv. Comput. Math. 44, No. 5, 1345--1383 (2018; Zbl 1406.35274) Full Text: DOI arXiv
Garcke, Harald; Lam, Kei Fong; Rocca, Elisabetta Optimal control of treatment time in a diffuse interface model of tumor growth. (English) Zbl 1403.35139 Appl. Math. Optim. 78, No. 3, 495-544 (2018). MSC: 35K61 49J20 49K20 92C37 92C50 PDFBibTeX XMLCite \textit{H. Garcke} et al., Appl. Math. Optim. 78, No. 3, 495--544 (2018; Zbl 1403.35139) Full Text: DOI arXiv
Dedè, Luca; Garcke, Harald; Lam, Kei Fong A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with different densities. (English) Zbl 1394.35353 J. Math. Fluid Mech. 20, No. 2, 531-567 (2018). MSC: 35Q35 76D27 76D45 76T99 76S05 35D30 PDFBibTeX XMLCite \textit{L. Dedè} et al., J. Math. Fluid Mech. 20, No. 2, 531--567 (2018; Zbl 1394.35353) Full Text: DOI arXiv
Garcke, Harald; Lam, Kei Fong; Nürnberg, Robert; Sitka, Emanuel A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis. (English) Zbl 1380.92029 Math. Models Methods Appl. Sci. 28, No. 3, 525-577 (2018). MSC: 92C50 35K57 35R35 65M60 PDFBibTeX XMLCite \textit{H. Garcke} et al., Math. Models Methods Appl. Sci. 28, No. 3, 525--577 (2018; Zbl 1380.92029) Full Text: DOI arXiv
Barrett, John W.; Garcke, Harald; Nürnberg, Robert Finite element approximation for the dynamics of fluidic two-phase biomembranes. (English) Zbl 1383.35153 ESAIM, Math. Model. Numer. Anal. 51, No. 6, 2319-2366 (2017). MSC: 35Q35 65M12 65M60 76D05 76D27 76M10 76Z99 92C05 PDFBibTeX XMLCite \textit{J. W. Barrett} et al., ESAIM, Math. Model. Numer. Anal. 51, No. 6, 2319--2366 (2017; Zbl 1383.35153) Full Text: DOI arXiv
Eck, Christof; Garcke, Harald; Knabner, Peter Mathematical modeling. (English) Zbl 1386.00063 Springer Undergraduate Mathematics Series. Cham: Springer (ISBN 978-3-319-55160-9/pbk; 978-3-319-55161-6/ebook). xv, 509 p. (2017). Reviewer: Yuriy V. Rogovchenko (Kristiansand) MSC: 00A71 93A30 34-01 35-01 49-01 PDFBibTeX XMLCite \textit{C. Eck} et al., Mathematical modeling. Cham: Springer (2017; Zbl 1386.00063) Full Text: DOI
Garcke, Harald; Hecht, Claudia; Hinze, Michael; Kahle, Christian; Lam, Kei Fong Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach. (English) Zbl 1352.49046 Interfaces Free Bound. 18, No. 2, 219-261 (2016). MSC: 49Q10 49Q12 35Q30 35Q35 35R35 PDFBibTeX XMLCite \textit{H. Garcke} et al., Interfaces Free Bound. 18, No. 2, 219--261 (2016; Zbl 1352.49046) Full Text: DOI arXiv
Blank, Luise; Garcke, Harald; Hecht, Claudia; Rupprecht, Christoph Sharp interface limit for a phase field model in structural optimization. (English) Zbl 1348.35259 SIAM J. Control Optim. 54, No. 3, 1558-1584 (2016). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q74 35R35 49Q10 49Q12 74B05 74P15 PDFBibTeX XMLCite \textit{L. Blank} et al., SIAM J. Control Optim. 54, No. 3, 1558--1584 (2016; Zbl 1348.35259) Full Text: DOI arXiv
Garcke, Harald; Hecht, Claudia Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow. (English) Zbl 1342.35218 ESAIM, Control Optim. Calc. Var. 22, No. 2, 309-337 (2016). Reviewer: Igor Bock (Bratislava) MSC: 35Q30 49Q10 35R35 49Q12 49Q20 76D05 PDFBibTeX XMLCite \textit{H. Garcke} and \textit{C. Hecht}, ESAIM, Control Optim. Calc. Var. 22, No. 2, 309--337 (2016; Zbl 1342.35218) Full Text: DOI arXiv
Garcke, Harald; Lam, Kei Fong; Sitka, Emanuel; Styles, Vanessa A Cahn-Hilliard-Darcy model for tumour growth with chemotaxis and active transport. (English) Zbl 1336.92038 Math. Models Methods Appl. Sci. 26, No. 6, 1095-1148 (2016). MSC: 92C50 92C17 35K57 35R35 65M60 PDFBibTeX XMLCite \textit{H. Garcke} et al., Math. Models Methods Appl. Sci. 26, No. 6, 1095--1148 (2016; Zbl 1336.92038) Full Text: DOI arXiv
Garcke, Harald; Hecht, Claudia Shape and topology optimization in Stokes flow with a phase field approach. (English) Zbl 1334.49133 Appl. Math. Optim. 73, No. 1, 23-70 (2016). MSC: 49Q10 49Q20 35R35 35Q35 76D07 PDFBibTeX XMLCite \textit{H. Garcke} and \textit{C. Hecht}, Appl. Math. Optim. 73, No. 1, 23--70 (2016; Zbl 1334.49133) Full Text: DOI Link
Garcke, Harald; Hecht, Claudia; Hinze, Michael; Kahle, Christian Numerical approximation of phase field based shape and topology optimization for fluids. (English) Zbl 1322.35113 SIAM J. Sci. Comput. 37, No. 4, A1846-A1871 (2015). Reviewer: Rodica Luca (Iaşi) MSC: 35Q35 35Q56 35R35 49Q10 65M12 65M22 65M60 65N15 76S05 76D05 PDFBibTeX XMLCite \textit{H. Garcke} et al., SIAM J. Sci. Comput. 37, No. 4, A1846--A1871 (2015; Zbl 1322.35113) Full Text: DOI arXiv
Barrett, John W.; Garcke, Harald; Nürnberg, Robert A stable parametric finite element discretization of two-phase Navier-Stokes flow. (English) Zbl 1320.76059 J. Sci. Comput. 63, No. 1, 78-117 (2015). MSC: 76M10 65M60 76D05 76Txx PDFBibTeX XMLCite \textit{J. W. Barrett} et al., J. Sci. Comput. 63, No. 1, 78--117 (2015; Zbl 1320.76059) Full Text: DOI arXiv
Barrett, John W.; Garcke, Harald; Nürnberg, Robert On the stable numerical approximation of two-phase flow with insoluble surfactant. (English) Zbl 1315.35156 ESAIM, Math. Model. Numer. Anal. 49, No. 2, 421-458 (2015). MSC: 35Q35 65M12 76D05 76D27 76M10 65M60 PDFBibTeX XMLCite \textit{J. W. Barrett} et al., ESAIM, Math. Model. Numer. Anal. 49, No. 2, 421--458 (2015; Zbl 1315.35156) Full Text: DOI arXiv
Barrett, John W.; Garcke, Harald; Nürnberg, Robert Phase field models versus parametric front tracking methods: are they accurate and computationally efficient? (English) Zbl 1388.65096 Commun. Comput. Phys. 15, No. 2, 506-555 (2014). MSC: 65M60 35K55 80A22 82C26 82C80 82D25 35R35 65M12 65M50 PDFBibTeX XMLCite \textit{J. W. Barrett} et al., Commun. Comput. Phys. 15, No. 2, 506--555 (2014; Zbl 1388.65096) Full Text: DOI arXiv
Garcke, Harald; Lam, Kei Fong; Stinner, Björn Diffuse interface modelling of soluble surfactants in two-phase flow. (English) Zbl 1319.35309 Commun. Math. Sci. 12, No. 8, 1475-1522 (2014). Reviewer: Baasansuren Jadamba (Rochester) MSC: 35R35 35R01 76T99 76D45 35C20 35Q35 PDFBibTeX XMLCite \textit{H. Garcke} et al., Commun. Math. Sci. 12, No. 8, 1475--1522 (2014; Zbl 1319.35309) Full Text: DOI arXiv
Abels, Helmut; Depner, Daniel; Garcke, Harald On an incompressible Navier-Stokes/Cahn-Hilliard system with degenerate mobility. (English) Zbl 1347.76052 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 30, No. 6, 1175-1190 (2013). MSC: 76T99 35Q30 35Q35 76D03 76D05 76D27 76D45 PDFBibTeX XMLCite \textit{H. Abels} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 30, No. 6, 1175--1190 (2013; Zbl 1347.76052) Full Text: DOI arXiv
Garcke, Harald Curvature driven interface evolution. (English) Zbl 1279.53064 Jahresber. Dtsch. Math.-Ver. 115, No. 2, 63-100 (2013). MSC: 53C44 35K93 35K91 35R35 35K55 49Q20 53A10 80A22 82B24 PDFBibTeX XMLCite \textit{H. Garcke}, Jahresber. Dtsch. Math.-Ver. 115, No. 2, 63--100 (2013; Zbl 1279.53064) Full Text: DOI
Abels, Helmut; Depner, Daniel; Garcke, Harald Existence of weak solutions for a diffuse interface model for two-phase flows of incompressible fluids with different densities. (English) Zbl 1273.76421 J. Math. Fluid Mech. 15, No. 3, 453-480 (2013). MSC: 76T99 35Q30 35Q35 76D03 76D05 76D27 76D45 PDFBibTeX XMLCite \textit{H. Abels} et al., J. Math. Fluid Mech. 15, No. 3, 453--480 (2013; Zbl 1273.76421) Full Text: DOI arXiv
Depner, Daniel; Garcke, Harald Linearized stability analysis of surface diffusion for hypersurfaces with triple lines. (English) Zbl 1263.35031 Hokkaido Math. J. 42, No. 1, 11-52 (2013). MSC: 35B35 35G30 35R35 35K55 53C44 PDFBibTeX XMLCite \textit{D. Depner} and \textit{H. Garcke}, Hokkaido Math. J. 42, No. 1, 11--52 (2013; Zbl 1263.35031) Full Text: DOI Euclid
Abels, Helmut; Garcke, Harald; Grün, Günther Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities. (English) Zbl 1242.76342 Math. Models Methods Appl. Sci. 22, No. 3, 1150013, 40 p. (2012). MSC: 76T99 35Q30 35Q35 35R35 76D05 76D45 80A22 PDFBibTeX XMLCite \textit{H. Abels} et al., Math. Models Methods Appl. Sci. 22, No. 3, 1150013, 40 p. (2012; Zbl 1242.76342) Full Text: DOI arXiv
Garcke, Harald; Schaubeck, Stefan Existence of weak solutions for the Stefan problem with anisotropic Gibbs-Thomson law. (English) Zbl 1235.35286 Adv. Math. Sci. Appl. 21, No. 1, 255-283 (2011). MSC: 35R35 35K55 35A15 80A22 35D30 PDFBibTeX XMLCite \textit{H. Garcke} and \textit{S. Schaubeck}, Adv. Math. Sci. Appl. 21, No. 1, 255--283 (2011; Zbl 1235.35286)
Garcke, Harald; Ito, Kazuo; Kohsaka, Yoshihito Surface diffusion with triple junctions: A stability criterion for stationary solutions. (English) Zbl 1228.35042 Adv. Differ. Equ. 15, No. 5-6, 437-472 (2010). Reviewer: Shengliang Pan (Shanghai) MSC: 35B35 35K55 35R35 53C44 35K35 PDFBibTeX XMLCite \textit{H. Garcke} et al., Adv. Differ. Equ. 15, No. 5--6, 437--472 (2010; Zbl 1228.35042)
Abels, Helmut; Garcke, Harald; Grün, Günther Thermodynamically Consistent Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities. arXiv:1011.0528 Preprint, arXiv:1011.0528 [physics.flu-dyn] (2010). MSC: 76T99 35Q30 35Q35 35R35 76D05 76D45 80A22 BibTeX Cite \textit{H. Abels} et al., ``Thermodynamically Consistent Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities'', Preprint, arXiv:1011.0528 [physics.flu-dyn] (2010) Full Text: arXiv OA License
Garcke, Harald; Ito, Kazuo; Kohsaka, Yoshihito Nonlinear stability of stationary solutions for surface diffusion with boundary conditions. (English) Zbl 1167.35005 SIAM J. Math. Anal. 40, No. 2, 491-515 (2008). Reviewer: Hans-Christoph Grunau (Magdeburg) MSC: 35B35 35R35 35K55 53C44 PDFBibTeX XMLCite \textit{H. Garcke} et al., SIAM J. Math. Anal. 40, No. 2, 491--515 (2008; Zbl 1167.35005) Full Text: DOI Link
Garcke, Harald; Wieland, Sandra Surfactant spreading on thin viscous films: nonnegative solutions of a coupled degenerate system. (English) Zbl 1102.35056 SIAM J. Math. Anal. 37, No. 6, 2025-2048 (2006). MSC: 35K65 35K35 76A20 76D08 35K55 35K50 PDFBibTeX XMLCite \textit{H. Garcke} and \textit{S. Wieland}, SIAM J. Math. Anal. 37, No. 6, 2025--2048 (2006; Zbl 1102.35056) Full Text: DOI Link
Garcke, Harald; Ito, Kazuo; Kohsaka, Yoshihito Linearized stability analysis of stationary solutions for surface diffusion with boundary conditions. (English) Zbl 1097.35030 SIAM J. Math. Anal. 36, No. 4, 1031-1056 (2005). Reviewer: Iuliana Oprea (Fort Collins) MSC: 35B35 35G30 35R35 PDFBibTeX XMLCite \textit{H. Garcke} et al., SIAM J. Math. Anal. 36, No. 4, 1031--1056 (2005; Zbl 1097.35030) Full Text: DOI
Escher, Joachim; Garcke, Harald; Ito, Kazuo Exponential stability for a mirror-symmetric three phase boundary motion by surface diffusion. (English) Zbl 1038.35012 Math. Nachr. 257, 3-15 (2003). MSC: 35B35 35G30 35K55 35R35 80A22 PDFBibTeX XMLCite \textit{J. Escher} et al., Math. Nachr. 257, 3--15 (2003; Zbl 1038.35012) Full Text: DOI
Garcke, Harald; Stoth, Barbara; Nestler, Britta Anisotropy in multi-phase systems: A phase field approach. (English) Zbl 0959.35169 Interfaces Free Bound. 1, No. 2, 175-198 (1999). MSC: 35R35 74A50 74N20 76T30 PDFBibTeX XMLCite \textit{H. Garcke} et al., Interfaces Free Bound. 1, No. 2, 175--198 (1999; Zbl 0959.35169) Full Text: DOI
Garcke, Harald; Sturzenhecker, Thomas The degenerate multi-phase Stefan problem with Gibbs-Thomson law. (English) Zbl 0921.35195 Adv. Math. Sci. Appl. 8, No. 2, 929-941 (1998). Reviewer: Marco Biroli (Monza) MSC: 35R35 80A22 PDFBibTeX XMLCite \textit{H. Garcke} and \textit{T. Sturzenhecker}, Adv. Math. Sci. Appl. 8, No. 2, 929--941 (1998; Zbl 0921.35195)
Bronsard, Lia; Garcke, Harald; Stoth, Barbara A multi-phase Mullins-Sekerka system: Matched asymptotic expansions and an implicit time discretisation for the geometric evolution problem. (English) Zbl 0924.35199 Proc. R. Soc. Edinb., Sect. A, Math. 128, No. 3, 481-506 (1998). MSC: 35R35 35Q35 35D05 76T99 PDFBibTeX XMLCite \textit{L. Bronsard} et al., Proc. R. Soc. Edinb., Sect. A, Math. 128, No. 3, 481--506 (1998; Zbl 0924.35199) Full Text: DOI