The general theme of this article is the theorical study of phase field systems, more precisely that of Caginalp. This work is motivated by their immense applications in many physical fields, industriels… The Caginalp problem gives the authors a formulation based on the fact that the phases separated by an unknown regular interface, which evolves in a regular way. The authors’ aim in this paper is to study on Caginalp for a conserved Phase-field with two temperatures. The authors have worked on the existence and uniqueness of the Caginalp phase field in a conservative version. Moreover, the authors have also used Dirichlet type boundary conditions with a regular potential; existence and uniqueness are analyzed by means of absorbing bounded sets. The authors build the solution of the conservative problem on the estimates which lead authors to treat the problem well to arrive at the result. These equations are known as the conserved phase-field based on type II heat conduction and two temperatures. The authors consider a regular potential, more precisely a polynomial with edge conditions of Dirichlet type. More precisely, the authors prove the existence and uniqueness of solutions.
| Published in | American Journal of Applied Mathematics (Volume 10, Issue 5) |
| DOI | 10.11648/j.ajam.20221005.12 |
| Page(s) | 205-211 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
A Conserved Phase-Field, Two Temperatures, Dirichlet Boundary Conditions, Regular Potential
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APA Style
Narcisse Batangouna, Cyr Séraphin Ngamouyih Moussata, Urbain Cyriaque Mavoungou. (2022). On the Caginalp for a Conserved Phase-Field with Two Temperatures. American Journal of Applied Mathematics, 10(5), 205-211. https://doi.org/10.11648/j.ajam.20221005.12
ACS Style
Narcisse Batangouna; Cyr Séraphin Ngamouyih Moussata; Urbain Cyriaque Mavoungou. On the Caginalp for a Conserved Phase-Field with Two Temperatures. Am. J. Appl. Math. 2022, 10(5), 205-211. doi: 10.11648/j.ajam.20221005.12
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Download@article{10.11648/j.ajam.20221005.12,
author = {Narcisse Batangouna and Cyr Séraphin Ngamouyih Moussata and Urbain Cyriaque Mavoungou},
title = {On the Caginalp for a Conserved Phase-Field with Two Temperatures},
journal = {American Journal of Applied Mathematics},
volume = {10},
number = {5},
pages = {205-211},
doi = {10.11648/j.ajam.20221005.12},
url = {https://doi.org/10.11648/j.ajam.20221005.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20221005.12},
abstract = {The general theme of this article is the theorical study of phase field systems, more precisely that of Caginalp. This work is motivated by their immense applications in many physical fields, industriels… The Caginalp problem gives the authors a formulation based on the fact that the phases separated by an unknown regular interface, which evolves in a regular way. The authors’ aim in this paper is to study on Caginalp for a conserved Phase-field with two temperatures. The authors have worked on the existence and uniqueness of the Caginalp phase field in a conservative version. Moreover, the authors have also used Dirichlet type boundary conditions with a regular potential; existence and uniqueness are analyzed by means of absorbing bounded sets. The authors build the solution of the conservative problem on the estimates which lead authors to treat the problem well to arrive at the result. These equations are known as the conserved phase-field based on type II heat conduction and two temperatures. The authors consider a regular potential, more precisely a polynomial with edge conditions of Dirichlet type. More precisely, the authors prove the existence and uniqueness of solutions.},
year = {2022}
}
TY - JOUR T1 - On the Caginalp for a Conserved Phase-Field with Two Temperatures AU - Narcisse Batangouna AU - Cyr Séraphin Ngamouyih Moussata AU - Urbain Cyriaque Mavoungou Y1 - 2022/10/24 PY - 2022 N1 - https://doi.org/10.11648/j.ajam.20221005.12 DO - 10.11648/j.ajam.20221005.12 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 205 EP - 211 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20221005.12 AB - The general theme of this article is the theorical study of phase field systems, more precisely that of Caginalp. This work is motivated by their immense applications in many physical fields, industriels… The Caginalp problem gives the authors a formulation based on the fact that the phases separated by an unknown regular interface, which evolves in a regular way. The authors’ aim in this paper is to study on Caginalp for a conserved Phase-field with two temperatures. The authors have worked on the existence and uniqueness of the Caginalp phase field in a conservative version. Moreover, the authors have also used Dirichlet type boundary conditions with a regular potential; existence and uniqueness are analyzed by means of absorbing bounded sets. The authors build the solution of the conservative problem on the estimates which lead authors to treat the problem well to arrive at the result. These equations are known as the conserved phase-field based on type II heat conduction and two temperatures. The authors consider a regular potential, more precisely a polynomial with edge conditions of Dirichlet type. More precisely, the authors prove the existence and uniqueness of solutions. VL - 10 IS - 5 ER -
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