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Research Article

The q-homotopy analysis method for a solution of the Cahn–Hilliard equation in the presence of advection and reaction terms

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Pages 813-819 | Received 23 Aug 2021, Accepted 26 Aug 2022, Published online: 12 Sep 2022

References

  • Akram U, Aly RS, Rizvi STR, et al. Traveling wave solutions for the fractional Wazwaz–Benjamin–Bona–Mahony model in arising shallow water waves. Results Phys. 2021;20:103725. doi:10.1016/j.rinp.2020.103725.
  • Rizvi ST, Seadawy AR, Ashraf F, et al. Lump and interaction solutions of a geophysical Korteweg–de Vries equation. Results Phys. 2020;19:Article 103661. doi:10.1016/j.rinp.2020.103661.
  • Younas U, Younis M, Aly RS, et al. Diverse exact solutions for modified nonlinear Schrödinger equation with conformable fractional derivative. Results Phys. 2021;20(8):Article 103766. doi:10.1016/j.rinp.2020.103766.
  • Younis M, Ali S, Rizvi STR, et al. Investigation of solitons and mixed lump wave solutions with (3 + 1)-dimensional potential-YTSF equation. Commun Nonlinear Sci Numer Simul. 2021;94:Article 105544. doi:10.1016/j.cnsns.2020.105544.
  • Ali A, Seadawy AR, Lu D. Soliton solutions of the nonlinear Schrödinger equation with the dual power law nonlinearity and resonant nonlinear schrödinger equation and their modulation instability analysis. Optik (Stuttg). 2017;145:79–88. doi:10.1016/j.ijleo.2017.07.016.
  • Aly RS, Younis M, Baber MZ, et al. Diverse acoustic wave propagation to confirmable time–space fractional KP equation arising in dusty plasma. Commun Theor Phys. 2021;73(11):Article 115004.
  • Younis M, Nadia C, Mahmood AS, et al. A variety of exact solutions to (2 + 1)-dimensional schrödinger equation. Waves Random Complex Media. 2018;30:1–10. doi:10.1080/17455030.2018.1532131.
  • Asghar A, Seadawy AR, Dianchen L. Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications. Open Physics. 2018;16(1):219–226. DOI: 10.1515/phys-2018-0032.
  • Dianchen L, Seadawy AR, Asghar A. Applications of exact traveling wave solutions of modified Liouville and the symmetric regularized long wave equations via two new techniques. Results Phys. 2018;9:1403–1410. doi:10.1016/j.rinp.2018.04.039.
  • Asghar A, Seadawy AR, Dianchen L. Dispersive solitary wave soliton solutions of (2 + 1)-dimensional Boussinesq dynamical equation via extended simple equation method. J King Saud Univ Sci. 2019;31(4):653–658. doi:10.1016/j.jksus.2017.12.015.
  • Alruwaili AD, Seadawy AR, Asghar A, et al. Novel analytical approach for the space-time fractional (2 + 1)-dimensional breaking soliton equation via mathematical methods. Mathematics. 2021;9:3253. doi:10.3390/math9243253.
  • Alruwaili AD, Seadawy AR, Ali A, et al. Soliton solutions of Calogero– Degasperis–Fokas dynamical equation via modified mathematical methods. Open Physics. 2022;20:174–187. DOI: 10.1515/phys-2022-0016.
  • Cahn JW, Hilliard J. Free energy of a nonuniform system. I. interfacial free energy. J Chem Phys. 1958;28:258–267.
  • Bertozzi AL, Esedoglu S, Gillette A. Inpainting of binary images using the Cahn-Hilliard equation. IEEE Trans Image Process. 2007;16(1):285–291. doi:10.1109/TIP.2006.887728.
  • Junseok K, Seunggyu L, Yongho C, et al. Basic principles and practical applications of the Cahn–Hilliard equation. Math Probl Eng. 2016: 11. Article ID 9532608. doi:10.1155/2016/9532608.
  • Miranville A, Piétrus A, Rakotoson J. Dynamical aspect of a generalized Cahn–Hilliard equation based on a microforce balance. Asymptotic Anal. 1998;16:315–345. Corpus ID:118719560.
  • Nicolaenko B, Scheurer B, Temam R. Some global dynamical properties of a class of pattern formation equations. Commun Partial Differ Equ. 1989;14(2):245–297. doi:10.1080/03605308908820597.
  • Novick-Cohen A, Segel LA. Nonlinear aspects of the Cahn-Hilliard equation. Physica D. 1984;10:277–298. doi:10.1016/0167-2789(84)90180-5.
  • Gurtin M. Generalised Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance. Physica D. 1996;92:178–192. doi:10.1016/0167-2789(95)00173-5.
  • Choksi R, Peletier MA, Williams JF. On the phase diagram for microphase separation of diblock copolymers: an approach via a nonlocal Cahn–Hilliard functional. SIAM J Appl Math. 2009;69:1712–1738. Doi:10.1137/080728809.
  • Tang P, Qiu F, Zhang H, et al. Phase separation patterns for diblock copolymers on spherical surfaces: a finite volume method. Phys Rev E Stat Nonlin Soft Matter Phys. 2005;72:016710. doi:10.1103/PhysRevE.72.016710.
  • Hu SY, Chen LQ. A phase-field model for evolving microstructures with strong elastic inhomogeneity. Acta Mater. 2001;49:1879–1890. doi:10.1016/S1359-6454(01)00118-5.
  • Bouhassoun A, Cherif H. Homotopy perturbation method For solving The fractional Cahn-Hilliard equation. J Interdiscip Math. 2015;18:513–524. doi:10.1080/10288457.2013.867627.
  • Tripathi NK, Das S, Ong SH, et al. Solution of time-fractional Cahn–Hilliard equation with reaction term using homotopy analysis method. Adv Mech Eng. 2017;9:168781401774077. doi:10.1177/1687814017740773.
  • Zhu J, Long-Qing C, Shen J, et al. Coarsening kinetics from a variable-mobility Cahn-Hilliard equation: application of a semi-implicit Fourier spectral method. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999;60:3564–3572. doi:10.1103/PhysRevE.60.3564.
  • Barrett J, Blowey J, Garcke H. Finite element approximation of the Cahn-Hilliard equation with degenerate mobility. SIAM J Numer Anal. 2000;37. doi:10.1137/S0036142997331669.
  • Berti A, Bochicchio I. A mathematical model for phase separation: a generalized Cahn- Hilliard equation. Math Method Appl Sci. 2011;34:1193–1203. doi:10.1002/mma.1432.
  • Wight CL, Zhao J. Solving Allen-Cahn and Cahn-Hilliard equations using the adaptive physics informed neural networks. Commun Comput Phys. 2021;29:930–954. doi:10.4208/cicp.OA-2020-0086.
  • Shah A, Siddiqui AA. Variational iteration method for the solution of viscous Cahn-Hilliard equation. World Appl Sci J. 2010;11(7):813–818. Corpus ID: 16027042.
  • Hussain S, Shah A. An analysis of two iterative techniques for solution of Cahn-Hilliard equation. Int J Nonlinear Sci. 2011;12(1):42–47.
  • Ugurlu Y, Kaya D. Solutions of the Cahn–Hilliard equation. Comput Math Appl. 2008;56:3038–3045. doi:10.1016/j.camwa.2008.07.007.
  • El-Tawil MA, Huseen S. The q-homotopy analysis method (q-HAM). Int J Appl Math Mech. 2012;8:51–75. Corpus ID:124341343.
  • Liao SJ. Beyond perturbation: introduction to the homotopy analysis method. Boca Raton (FL): CRC Press, Chapman & Hall; 2003.