Robust exponential attractors for a parabolic–hyperbolic phase-field system
Abstract In this paper, we construct a robust family of exponential attractors for a parabolic–hyperbolic phase-field system (PHPFS), which describes phase separation in material sciences, e.g., melting and solidification. A consequence of this is the existence of finite fractal dimensional global a...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-09-01
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| Series: | Boundary Value Problems |
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| Online Access: | http://link.springer.com/article/10.1186/s13661-018-1061-4 |
| _version_ | 1818241935146483712 |
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| author | Cyril D. Enyi |
| author_facet | Cyril D. Enyi |
| author_sort | Cyril D. Enyi |
| collection | DOAJ |
| description | Abstract In this paper, we construct a robust family of exponential attractors for a parabolic–hyperbolic phase-field system (PHPFS), which describes phase separation in material sciences, e.g., melting and solidification. A consequence of this is the existence of finite fractal dimensional global attractors which are both upper and lower semicontinuous at the parameter ϵ=0 $\epsilon=0$. Hence we establish the convergence of the dynamics of PHPFS to those of the well known Cagilnap phase-field system. |
| first_indexed | 2024-12-12T13:37:14Z |
| format | Article |
| id | doaj.art-c23e30273ecf4d3e9fabfa9ed3cb7c62 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-12T13:37:14Z |
| publishDate | 2018-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-c23e30273ecf4d3e9fabfa9ed3cb7c622022-12-22T00:22:55ZengSpringerOpenBoundary Value Problems1687-27702018-09-012018111710.1186/s13661-018-1061-4Robust exponential attractors for a parabolic–hyperbolic phase-field systemCyril D. Enyi0College of Sciences, Department of Mathematics, University of Hafr Al BatinAbstract In this paper, we construct a robust family of exponential attractors for a parabolic–hyperbolic phase-field system (PHPFS), which describes phase separation in material sciences, e.g., melting and solidification. A consequence of this is the existence of finite fractal dimensional global attractors which are both upper and lower semicontinuous at the parameter ϵ=0 $\epsilon=0$. Hence we establish the convergence of the dynamics of PHPFS to those of the well known Cagilnap phase-field system.http://link.springer.com/article/10.1186/s13661-018-1061-4Parabolic–hyperbolic phase-field systemExponential attractorsContinuity |
| spellingShingle | Cyril D. Enyi Robust exponential attractors for a parabolic–hyperbolic phase-field system Boundary Value Problems Parabolic–hyperbolic phase-field system Exponential attractors Continuity |
| title | Robust exponential attractors for a parabolic–hyperbolic phase-field system |
| title_full | Robust exponential attractors for a parabolic–hyperbolic phase-field system |
| title_fullStr | Robust exponential attractors for a parabolic–hyperbolic phase-field system |
| title_full_unstemmed | Robust exponential attractors for a parabolic–hyperbolic phase-field system |
| title_short | Robust exponential attractors for a parabolic–hyperbolic phase-field system |
| title_sort | robust exponential attractors for a parabolic hyperbolic phase field system |
| topic | Parabolic–hyperbolic phase-field system Exponential attractors Continuity |
| url | http://link.springer.com/article/10.1186/s13661-018-1061-4 |
| work_keys_str_mv | AT cyrildenyi robustexponentialattractorsforaparabolichyperbolicphasefieldsystem |