On a non-isothermal Cahn-Hilliard model based on a microforce balance

Marveggio A, Schimperna G. 2021. On a non-isothermal Cahn-Hilliard model based on a microforce balance. Journal of Differential Equations. 274(2), 924–970.


Journal Article | Published | English

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Author
Marveggio, AliceIST Austria; Schimperna, Giulio
Department
Abstract
This paper is concerned with a non-isothermal Cahn-Hilliard model based on a microforce balance. The model was derived by A. Miranville and G. Schimperna starting from the two fundamental laws of Thermodynamics, following M. Gurtin's two-scale approach. The main working assumptions are made on the behaviour of the heat flux as the absolute temperature tends to zero and to infinity. A suitable Ginzburg-Landau free energy is considered. Global-in-time existence for the initial-boundary value problem associated to the entropy formulation and, in a subcase, also to the weak formulation of the model is proved by deriving suitable a priori estimates and by showing weak sequential stability of families of approximating solutions. At last, some highlights are given regarding a possible approximation scheme compatible with the a-priori estimates available for the system.
Publishing Year
Date Published
2021-02-15
Journal Title
Journal of Differential Equations
Acknowledgement
G. Schimperna has been partially supported by GNAMPA (Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica).
Volume
274
Issue
2
Page
924-970
ISSN
eISSN
IST-REx-ID

Cite this

Marveggio A, Schimperna G. On a non-isothermal Cahn-Hilliard model based on a microforce balance. Journal of Differential Equations. 2021;274(2):924-970. doi:10.1016/j.jde.2020.10.030
Marveggio, A., & Schimperna, G. (2021). On a non-isothermal Cahn-Hilliard model based on a microforce balance. Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2020.10.030
Marveggio, Alice, and Giulio Schimperna. “On a Non-Isothermal Cahn-Hilliard Model Based on a Microforce Balance.” Journal of Differential Equations. Elsevier, 2021. https://doi.org/10.1016/j.jde.2020.10.030.
A. Marveggio and G. Schimperna, “On a non-isothermal Cahn-Hilliard model based on a microforce balance,” Journal of Differential Equations, vol. 274, no. 2. Elsevier, pp. 924–970, 2021.
Marveggio A, Schimperna G. 2021. On a non-isothermal Cahn-Hilliard model based on a microforce balance. Journal of Differential Equations. 274(2), 924–970.
Marveggio, Alice, and Giulio Schimperna. “On a Non-Isothermal Cahn-Hilliard Model Based on a Microforce Balance.” Journal of Differential Equations, vol. 274, no. 2, Elsevier, 2021, pp. 924–70, doi:10.1016/j.jde.2020.10.030.
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