Zhang, Jiahao; Zhang, Shiheng; Shen, Jie; Lin, Guang Energy-dissipative evolutionary deep operator neural networks. (English) Zbl 07797626 J. Comput. Phys. 498, Article ID 112638, 17 p. (2024). MSC: 68Txx 65Nxx 35Rxx PDFBibTeX XMLCite \textit{J. Zhang} et al., J. Comput. Phys. 498, Article ID 112638, 17 p. (2024; Zbl 07797626) Full Text: DOI arXiv
Moser, Maximilian Convergence of the scalar- and vector-valued Allen-Cahn equation to mean curvature flow with \(90^{\circ}\)-contact angle in higher dimensions. I: Convergence result. (English) Zbl 1510.35027 Asymptotic Anal. 131, No. 3-4, 297-383 (2023). MSC: 35B25 35K20 35K57 53E10 PDFBibTeX XMLCite \textit{M. Moser}, Asymptotic Anal. 131, No. 3--4, 297--383 (2023; Zbl 1510.35027) Full Text: DOI arXiv
Bretin, Elie; Masnou, Simon; Sengers, Arnaud; Terii, Garry Approximation of surface diffusion flow: a second-order variational Cahn-Hilliard model with degenerate mobilities. (English) Zbl 1492.74124 Math. Models Methods Appl. Sci. 32, No. 4, 793-829 (2022). MSC: 74N20 74A50 74S25 74H10 PDFBibTeX XMLCite \textit{E. Bretin} et al., Math. Models Methods Appl. Sci. 32, No. 4, 793--829 (2022; Zbl 1492.74124) Full Text: DOI arXiv
Abels, Helmut; Moser, Maximilian Convergence of the Allen-Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to \(90^\circ\). (English) Zbl 1485.35020 SIAM J. Math. Anal. 54, No. 1, 114-172 (2022). Reviewer: Kelei Wang (Wuhan) MSC: 35B25 35B36 35K57 35K61 35R37 53E10 PDFBibTeX XMLCite \textit{H. Abels} and \textit{M. Moser}, SIAM J. Math. Anal. 54, No. 1, 114--172 (2022; Zbl 1485.35020) Full Text: DOI arXiv
Hester, Eric W.; Vasil, Geoffrey M.; Burns, Keaton J. Improving accuracy of volume penalised fluid-solid interactions. (English) Zbl 07506520 J. Comput. Phys. 430, Article ID 110043, 25 p. (2021). MSC: 76Dxx 76Mxx 76-XX PDFBibTeX XMLCite \textit{E. W. Hester} et al., J. Comput. Phys. 430, Article ID 110043, 25 p. (2021; Zbl 07506520) Full Text: DOI arXiv
Bures, Miguel; Moure, Adrian; Gomez, Hector Computational treatment of interface dynamics via phase-field modeling. (English) Zbl 1481.76263 Greiner, David (ed.) et al., Numerical simulation in physics and engineering: trends and applications. Lecture notes of the XVIII ‘Jacques-Louis Lions’ Spanish-French school, Las Palmas de Gran Canaria, Spain, June 25–29, 2018. Cham: Springer. SEMA SIMAI Springer Ser. 24, 81-118 (2021). MSC: 76T99 76M99 65D07 80A22 PDFBibTeX XMLCite \textit{M. Bures} et al., SEMA SIMAI Springer Ser. 24, 81--118 (2021; Zbl 1481.76263) Full Text: DOI
Hester, Eric W.; Couston, Louis-Alexandre; Favier, Benjamin; Burns, Keaton J.; Vasil, Geoffrey M. Improved phase-field models of melting and dissolution in multi-component flows. (English) Zbl 1472.76105 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2242, Article ID 20200508, 22 p. (2020). MSC: 76T06 82C24 PDFBibTeX XMLCite \textit{E. W. Hester} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2242, Article ID 20200508, 22 p. (2020; Zbl 1472.76105) Full Text: DOI arXiv
Abels, Helmut; Moser, Maximilian Convergence of the Allen-Cahn equation to the mean curvature flow with \(90^\circ\)-contact angle in 2D. (English) Zbl 1430.35127 Interfaces Free Bound. 21, No. 3, 313-365 (2019). Reviewer: Joseph Shomberg (Providence) MSC: 35K57 35B25 35B36 35R37 35Q35 53E10 PDFBibTeX XMLCite \textit{H. Abels} and \textit{M. Moser}, Interfaces Free Bound. 21, No. 3, 313--365 (2019; Zbl 1430.35127) Full Text: DOI arXiv
Alber, Hans-Dieter Asymptotics and numerical efficiency of the Allen-Cahn model for phase interfaces with low energy in solids. (English) Zbl 1375.74075 Contin. Mech. Thermodyn. 29, No. 3, 757-803 (2017). MSC: 74N20 PDFBibTeX XMLCite \textit{H.-D. Alber}, Contin. Mech. Thermodyn. 29, No. 3, 757--803 (2017; Zbl 1375.74075) Full Text: DOI arXiv
Lee, Dongsun; Kim, Junseok Comparison study of the conservative Allen-Cahn and the Cahn-Hilliard equations. (English) Zbl 07313590 Math. Comput. Simul. 119, 35-56 (2016). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{D. Lee} and \textit{J. Kim}, Math. Comput. Simul. 119, 35--56 (2016; Zbl 07313590) Full Text: DOI
Gonzalez-Ferreiro, Borja; Gomez, H.; Romero, Ignacio A thermodynamically consistent numerical method for a phase field model of solidification. (English) Zbl 1457.80008 Commun. Nonlinear Sci. Numer. Simul. 19, No. 7, 2309-2323 (2014). MSC: 80A22 65M60 PDFBibTeX XMLCite \textit{B. Gonzalez-Ferreiro} et al., Commun. Nonlinear Sci. Numer. Simul. 19, No. 7, 2309--2323 (2014; Zbl 1457.80008) Full Text: DOI
Alber, Hans-Dieter; Zhu, Peicheng Comparison of a rapidely converging phase field model for interfaces in solids with the Allen-Cahn model. (English) Zbl 1272.35031 J. Elasticity 111, No. 2, 153-221 (2013). MSC: 35B40 35C20 35Q74 74H10 74N20 PDFBibTeX XMLCite \textit{H.-D. Alber} and \textit{P. Zhu}, J. Elasticity 111, No. 2, 153--221 (2013; Zbl 1272.35031) Full Text: DOI
Chen, Xinfu; Caginalp, Gunduz; Esenturk, Emre Interface conditions for a phase field model with anisotropic and non-local interactions. (English) Zbl 1256.35209 Arch. Ration. Mech. Anal. 202, No. 2, 349-372 (2011). MSC: 35R35 74N20 35Q79 80A22 PDFBibTeX XMLCite \textit{X. Chen} et al., Arch. Ration. Mech. Anal. 202, No. 2, 349--372 (2011; Zbl 1256.35209) Full Text: DOI