{"doi":"10.1016/j.jde.2020.10.030","publication":"Journal of Differential Equations","main_file_link":[{"url":"https://arxiv.org/abs/2004.02618","open_access":"1"}],"article_type":"original","publication_identifier":{"eissn":["10902732"],"issn":["00220396"]},"intvolume":"       274","day":"15","date_updated":"2023-08-04T11:12:16Z","language":[{"iso":"eng"}],"year":"2021","oa":1,"external_id":{"isi":["000600845300023"],"arxiv":["2004.02618"]},"abstract":[{"text":"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.","lang":"eng"}],"publisher":"Elsevier","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"oa_version":"Preprint","page":"924-970","type":"journal_article","article_processing_charge":"No","department":[{"_id":"JuFi"}],"issue":"2","publication_status":"published","quality_controlled":"1","volume":274,"status":"public","_id":"8792","month":"02","author":[{"id":"25647992-AA84-11E9-9D75-8427E6697425","first_name":"Alice","last_name":"Marveggio","full_name":"Marveggio, Alice"},{"full_name":"Schimperna, Giulio","last_name":"Schimperna","first_name":"Giulio"}],"citation":{"short":"A. Marveggio, G. Schimperna, Journal of Differential Equations 274 (2021) 924–970.","chicago":"Marveggio, Alice, and Giulio Schimperna. “On a Non-Isothermal Cahn-Hilliard Model Based on a Microforce Balance.” <i>Journal of Differential Equations</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.jde.2020.10.030\">https://doi.org/10.1016/j.jde.2020.10.030</a>.","ama":"Marveggio A, Schimperna G. On a non-isothermal Cahn-Hilliard model based on a microforce balance. <i>Journal of Differential Equations</i>. 2021;274(2):924-970. doi:<a href=\"https://doi.org/10.1016/j.jde.2020.10.030\">10.1016/j.jde.2020.10.030</a>","ista":"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.","ieee":"A. Marveggio and G. Schimperna, “On a non-isothermal Cahn-Hilliard model based on a microforce balance,” <i>Journal of Differential Equations</i>, vol. 274, no. 2. Elsevier, pp. 924–970, 2021.","apa":"Marveggio, A., &#38; Schimperna, G. (2021). On a non-isothermal Cahn-Hilliard model based on a microforce balance. <i>Journal of Differential Equations</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jde.2020.10.030\">https://doi.org/10.1016/j.jde.2020.10.030</a>","mla":"Marveggio, Alice, and Giulio Schimperna. “On a Non-Isothermal Cahn-Hilliard Model Based on a Microforce Balance.” <i>Journal of Differential Equations</i>, vol. 274, no. 2, Elsevier, 2021, pp. 924–70, doi:<a href=\"https://doi.org/10.1016/j.jde.2020.10.030\">10.1016/j.jde.2020.10.030</a>."},"date_created":"2020-11-22T23:01:26Z","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).","scopus_import":"1","title":"On a non-isothermal Cahn-Hilliard model based on a microforce balance","date_published":"2021-02-15T00:00:00Z"}