On a generalization of the Cahn-Hilliard type equation with logarithmic nonlinearities for formation of islands

[1] Cahn J.W., On spinodal decomposition, Acta Metallurgica, 9(9), 795–801, 1961. CahnJ.W. On spinodal decomposition Acta Metallurgica 9 9 795 801 1961 Search in Google Scholar

[2] Cahn J.W., Hilliard J.E., Free energy of a nonuniform system I. Interfacial free energy, The Journal of Chemical Physics, 28(2), 258–267, 1958. CahnJ.W. HilliardJ.E. Free energy of a nonuniform system I. Interfacial free energy The Journal of Chemical Physics 28 2 258 267 1958 Search in Google Scholar

[3] Cherfils L., Miranville A., Zelik S., The Cahn–Hilliard equation with logarithmic potentials, Milan Journal of Mathematics, 79, 561–596, 2011. CherfilsL. MiranvilleA. ZelikS. The Cahn–Hilliard equation with logarithmic potentials Milan Journal of Mathematics 79 561 596 2011 Search in Google Scholar

[4] Elliott C.M., French D.A., Milner F.A., A second order splitting method for the Cahn–Hilliard equation, Numerische Mathematik, 54, 575–590, 1989. ElliottC.M. FrenchD.A. MilnerF.A. A second order splitting method for the Cahn–Hilliard equation Numerische Mathematik 54 575 590 1989 Search in Google Scholar

[5] Novick-Cohen A., The Cahn–Hilliard equation: mathematical and modeling perspectives, Advances in Mathematical Sciences and Applications, 8(2), 965–985, 1998. Novick-CohenA. The Cahn–Hilliard equation: mathematical and modeling perspectives Advances in Mathematical Sciences and Applications 8 2 965 985 1998 Search in Google Scholar

[6] Cohen D.S., Murray J.D., A generalized diffusion model for growth and dispersal in a population, Journal of Mathematical Biology, 12(2), 237–249, 1981. CohenD.S. MurrayJ.D. A generalized diffusion model for growth and dispersal in a population Journal of Mathematical Biology 12 2 237 249 1981 Search in Google Scholar

[7] Klapper I., Dockery J., Role of cohesion in the material description of biofilms, Physical Review E, 74, 031902, 2006. KlapperI. DockeryJ. Role of cohesion in the material description of biofilms Physical Review E 74 031902 2006 Search in Google Scholar

[8] Oron A., Davis S.H., Bankoff S.G., Long-scale evolution of thin liquid films, Reviews of Modern Physics, 69, 931–980, 1997. OronA. DavisS.H. BankoffS.G. Long-scale evolution of thin liquid films Reviews of Modern Physics 69 931 980 1997 Search in Google Scholar

[9] Thiele U., Knobloch E., Thin liquid films on a slightly inclined heated plate, Physica D: Nonlinear Phenomena, 190(3–4), 213–248, 2004. ThieleU. KnoblochE. Thin liquid films on a slightly inclined heated plate Physica D: Nonlinear Phenomena 190 3–4 213 248 2004 Search in Google Scholar

[10] Chalupecký V., Numerical studies of Cahn–Hilliard equation and applications in image processing, Proceedings of Gzech-Japanese Seminar in Applied Mathematics, Czech Technical University, Prague, Czechia, 2004. ChalupeckýV. Numerical studies of Cahn–Hilliard equation and applications in image processing Proceedings of Gzech-Japanese Seminar in Applied Mathematics Czech Technical University, Prague, Czechia 2004 Search in Google Scholar

[11] Dolcetta I.C., Vita S.F., March R., Area-preserving curve-shortening flows: from phase separation to image processing, Interfaces and Free Boundaries, 4(4), 325–343, 2002. DolcettaI.C. VitaS.F. MarchR. Area-preserving curve-shortening flows: from phase separation to image processing Interfaces and Free Boundaries 4 4 325 343 2002 Search in Google Scholar

[12] Tremaine S., On the origin of irregular structure in Saturn’s rings, The Astronomical Journal, 125, 894–901, 2003. TremaineS. On the origin of irregular structure in Saturn’s rings The Astronomical Journal 125 894 901 2003 Search in Google Scholar

[13] Cherfils L., Miranville A., Zelik S., On a generalized Cahn–Hilliard equation with biological applications, Discrete and Continuous Dynamical Systems-B, 19(7), 2013–2026, 2014. CherfilsL. MiranvilleA. ZelikS. On a generalized Cahn–Hilliard equation with biological applications Discrete and Continuous Dynamical Systems-B 19 7 2013 2026 2014 Search in Google Scholar

[14] Khain E., Sander L.M., Generalized Cahn–Hilliard equation for biological applications, Physical Review E, 77, 051129, 2008. KhainE. SanderL.M. Generalized Cahn–Hilliard equation for biological applications Physical Review E 77 051129 2008 Search in Google Scholar

[15] Fakih H., A Cahn–Hilliard equation with a proliferation term for biological and chemical applications, Asymptotic Analysis, 94(1–2), 71–104, 2015. FakihH. A Cahn–Hilliard equation with a proliferation term for biological and chemical applications Asymptotic Analysis 94 1–2 71 104 2015 Search in Google Scholar

[16] Miranville A., Existence of solutions to a Cahn-Hilliard type equation with a logarithmic nonlinear term, Mediterranean Journal of Mathematics, 16, 6, 2019. MiranvilleA. Existence of solutions to a Cahn-Hilliard type equation with a logarithmic nonlinear term Mediterranean Journal of Mathematics 16 6 2019 Search in Google Scholar

[17] Oono Y., Puri S., Computationally efficient modeling of ordering of quenched phases, Physical Review Letters, 58, 836–839, 1987. OonoY. PuriS. Computationally efficient modeling of ordering of quenched phases Physical Review Letters 58 836 839 1987 Search in Google Scholar

[18] Miranville A., Asymptotic behavior of the Cahn–Hilliard-Oono equation, Journal of Applied Analysis and Computation, 1(4), 523–536, 2011. MiranvilleA. Asymptotic behavior of the Cahn–Hilliard-Oono equation Journal of Applied Analysis and Computation 1 4 523 536 2011 Search in Google Scholar

[19] Miranville A., Asymptotic behavior of a generalized Cahn–Hilliard equation with a proliferation term, Applicable Analysis, 92(6), 1308–1321, 2013. MiranvilleA. Asymptotic behavior of a generalized Cahn–Hilliard equation with a proliferation term Applicable Analysis 92 6 1308 1321 2013 Search in Google Scholar

[20] Fakih H., Asymptotic behavior of a generalized Cahn–Hilliard equation with a mass source, Applicable Analysis, 96(2), 324–348, 2017. FakihH. Asymptotic behavior of a generalized Cahn–Hilliard equation with a mass source Applicable Analysis 96 2 324 348 2017 Search in Google Scholar

[21] Miranville A., The Cahn-Hilliard equation and some of its variants, AIMS Mathematics, 2(3), 479–544, 2017. MiranvilleA. The Cahn-Hilliard equation and some of its variants AIMS Mathematics 2 3 479 544 2017 Search in Google Scholar

[22] Fakih H., Mghames R., Nasreddine N., On the Cahn–Hilliard equation with mass source for biological applications, Communications on Pure and Applied Analysis, 20(2), 495–510, 2021. FakihH. MghamesR. NasreddineN. On the Cahn–Hilliard equation with mass source for biological applications Communications on Pure and Applied Analysis 20 2 495 510 2021 Search in Google Scholar

[23] Bertozzi A., Esedoğlu S., Gillette A., Analysis of a two-scale Cahn-Hilliard model for binary image inpainting, Multi-scale Modeling and Simulations, 6(3), 913–936, 2007. BertozziA. EsedoğluS. GilletteA. Analysis of a two-scale Cahn-Hilliard model for binary image inpainting Multi-scale Modeling and Simulations 6 3 913 936 2007 Search in Google Scholar

[24] Cherfils L., Fakih H., Miranville A., Finite-dimensional attractors for the Bertozzi–Esedoglu–Gillette–Cahn–Hilliard equation in image inpainting, Inverse Problems and Imaging, 9(1), 105–125, 2015. CherfilsL. FakihH. MiranvilleA. Finite-dimensional attractors for the Bertozzi–Esedoglu–Gillette–Cahn–Hilliard equation in image inpainting Inverse Problems and Imaging 9 1 105 125 2015 Search in Google Scholar

[25] Cherfils L., Fakih H., Miranville A., A Cahn–Hilliard system with a fidelity term for color image inpainting, Journal of Mathematical Imaging and Vision, 54, 117–131, 2016. CherfilsL. FakihH. MiranvilleA. A Cahn–Hilliard system with a fidelity term for color image inpainting Journal of Mathematical Imaging and Vision 54 117 131 2016 Search in Google Scholar

[26] Cherfils L., Fakih H., Miranville A., A complex version of the Cahn-Hilliard equation for grayscale image inpainting, Multiscale Modeling and Simulations, 15(1), 575–605, 2017. CherfilsL. FakihH. MiranvilleA. A complex version of the Cahn-Hilliard equation for grayscale image inpainting Multiscale Modeling and Simulations 15 1 575 605 2017 Search in Google Scholar

[27] Awad Y., Fakih H., Alkhezi Y., Numerical linear algebra for the two-dimensional Bertozzi-Esedoglu-Gillette-Cahn-Hilliard equation in image inpainting, Mathematics, 11(24), 4952, 2023. AwadY. FakihH. AlkheziY. Numerical linear algebra for the two-dimensional Bertozzi-Esedoglu-Gillette-Cahn-Hilliard equation in image inpainting Mathematics 11 24 4952 2023 Search in Google Scholar

[28] Cherfils L., Fakih H., Miranville A., On the Bertozzi–Esedoglu–Gillette–Cahn–Hilliard equation with logarithmic nonlinear terms, SIAM Journal of Imaging Sciences, 8(2), 1123–1140, 2015. CherfilsL. FakihH. MiranvilleA. On the Bertozzi–Esedoglu–Gillette–Cahn–Hilliard equation with logarithmic nonlinear terms SIAM Journal of Imaging Sciences 8 2 1123 1140 2015 Search in Google Scholar