International Journal of Numerical Methods and Applications

The International Journal of Numerical Methods and Applications publishes research articles on numerical methods and their applications in various fields, including differential equations, fluid dynamics, and bioinformatics. It also welcomes survey articles on new methods in numerical analysis.

Submit Article

EXISTENCE OF THE GLOBAL ATTRACTOR FOR A HYPERBOLIC PHASE FIELD SYSTEM OF CAGINALP TYPE WITH RELAXATION, GOVERNED BY A POLYNOMIAL GROWTH POTENTIAL OF DEGREE $2p-1$

Authors

  • Brice Landry DOUMBE BANGOLA
  • Mohamed Ali IPOPA
  • Jean De Dieu MANGOUBI
  • Franck Davhys Reval LANGA

Keywords:

Cahn-Hilliard parabolic-hyperbolic phase field system, regular potential, Dirichlet boundary conditions

DOI:

https://doi.org/10.17654/0975045225001

Abstract

Phase field systems have attracted the attention of many researchers in physics and mathematics for several years. They have a wide range of applications, including materials science, thermal welding, crystal formation, and others. In such phenomena, perturbations can occur. The industrial world seeks to understand the behavior of the perturbed system while seeking better control of the perturbation. Our goal in this paper is to study the asymptotic behavior of the solution, proving the existence of the global attractor for perturbed phase field systems with a regular potential and polynomial growth typically of degree $2p - 1$.

Received: August 7, 2024
Revised: September 5, 2024
Accepted: September 14, 2024

References

S. Agmon, Lectures on elliptic boundary value problems, Mathematical Studies, Van Nostrand, New York, 1965.

D. Brochet, D. Hilhorst and A. Novick-Cohen, Maximal attractor and inertial sets for a conserved phase-field model, Adv. Differential Equations 1 (1996), 547-578.

G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Rational Mech. Anal. 92 (1986), 205-245.

G. Caginalp, The dynamics of a conserved phase-field system; Stefan-like, Hele-Shaw and Cahn-Hilliard models as asymptotic limits, IMA J. Appl. Math. 44 (1990), 77-94.

G. Caginalp, Conserved-phase field system: implications for kinetic undercooling, Physical Review B 38 (1988), 789-791.

M. Grasseli, A. Miranville, V. Pata and S. Zelik, Well-posedness and long time behavior of parabolic-hyperbolic phase-field system with singular potentials, Math. Nachr. 280 (2007), 13-14.

M. E. I. Goyaud, F. Moukamba, D. Moukoko and F. D. R. Langa, Existence and uniqueness of solution for Caginalp phase field system with polynomial growth potential, Int. Math. Forum 10 (2015), 477-486.

F. D. R. Langa, D. Moukoko, D. Ampini and F. Moukamba, Existence and uniqueness of solution for Caginalp hyperbolic phase-field system with a polynomial potential, Journal of Mathematics Research 10(1) (2018), 124-131.

Mangoubi Jean De Dieu, Daniel Moukoko, Dieudonne Ampini and Fidele Moukamba, Existence of global attractor for Cahn-Hilliard perturbed phase-field system with Dirichlet boundary condition and regular potential, Journal of Advances in Mathematics and Computer Science 26(6) (2018), 1-20.

Mavoungou Cyriaque Urbain, D. Moukoko, F. D. R. Langa and D. Ampini, Existence and uniqueness of solution hyperbolic relaxation for Caginalp phase-field system with singular potential, Asymptot. Anal. 116 (2020), 41-72. DOI 10.3233/ASY-191539.

Mavoungou Cyriaque Urbain, F. D. R. Langa and D. Moukoko, Study of the dissipativity, global attractor and exponential for a hyperbolic relaxation for Caginalp phase-field system with singular nonlinear terms, Asymptot. Anal. 125 (2021) 159-186. DOI 10.3233/ASY-201655.

I. Mayeul Evrard, D. Moukoko, F. Moukamba and F. D. R. Langa, Existence of global attractor for hyperbolics field-phase system of Caginalp type with polynomial growth potential, British Journal of Mathematics and Computer Science 18(6) (2016), 1-18.

A. Miranville and S. Zelik, Attractors for dissipative partial differential equations in bounded and unbounded domains, Handbook of Differential Equations, Evolutionary Partial Differential Equations, C. M. Dafermos and M. Pokorny, eds., Elsevier, Amsterdam, Vol. 4, 2008, pp. 103-200.

D. Moukoko, Well-posedness and longtime behaviors of a hyperbolic Caginalp system, Journal of Applied Analysis and Computation 4 (2014), 151-196.

R. Temam, Infinite-dimensional dynamical systems in mechanics and physics, 2nd ed., Applied Mathematical Sciences, Springer-Verlag, New York, Vol. 68, 1997.

Downloads

Published

2024-10-08

Issue

Vol. 25 No. 1 (2025)

Section

Articles

License

Copyright (c) 2024 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Licensing Terms:

Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.

Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.

No Derivatives: Modifying or creating derivative works not allowed without written permission.

Contact Pushpa Publishing House for more info or permissions.

How to Cite

EXISTENCE OF THE GLOBAL ATTRACTOR FOR A HYPERBOLIC PHASE FIELD SYSTEM OF CAGINALP TYPE WITH RELAXATION, GOVERNED BY A POLYNOMIAL GROWTH POTENTIAL OF DEGREE $2p-1$. (2024). International Journal of Numerical Methods and Applications, 25(1), 1-40. https://doi.org/10.17654/0975045225001

Similar Articles

1-10 of 34

You may also start an advanced similarity search for this article.