We consider a non-isothermal modified viscous Cahn-Hilliard equation which was previously analyzed by M. Grasselli et al. Such an equation is characterized by an inertial term and it is coupled with a hyperbolic heat equation from the Maxwell-Cattaneo's law. We analyze the case in which the order parameter is subject to a dynamic boundary condition. This assumption requires a more refined strategy to extend the previous results to the present case. More precisely, we first prove the well-posedness for solutions with finite energy as well as for weak solutions. Then we establish the existence of a global attractor. Finally, we prove the convergence of any given weak solution to a single equilibrium by using a suitable Lojasiewicz-Simon inequality.

Non-isothermal viscous Cahn-Hilliard equation with inertial term and dynamic boundary conditions / C. Cavaterra, M. Grasselli, H. Wu. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 13:5(2014), pp. 1855-1890.

Non-isothermal viscous Cahn-Hilliard equation with inertial term and dynamic boundary conditions

C. Cavaterra
Primo
;
2014

Abstract

We consider a non-isothermal modified viscous Cahn-Hilliard equation which was previously analyzed by M. Grasselli et al. Such an equation is characterized by an inertial term and it is coupled with a hyperbolic heat equation from the Maxwell-Cattaneo's law. We analyze the case in which the order parameter is subject to a dynamic boundary condition. This assumption requires a more refined strategy to extend the previous results to the present case. More precisely, we first prove the well-posedness for solutions with finite energy as well as for weak solutions. Then we establish the existence of a global attractor. Finally, we prove the convergence of any given weak solution to a single equilibrium by using a suitable Lojasiewicz-Simon inequality.
Cattaneo's law; Convergence to equilibrium; Existence and uniqueness; Global attractors; Inertial term; Viscous Cahn-Hilliard equation
Settore MAT/05 - Analisi Matematica
2014
Article (author)
File in questo prodotto:
File Dimensione Formato  
1534-0392_2014_5_1855.pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 583.15 kB
Formato Adobe PDF
583.15 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
CAVATERRA_GRASSELLI_WU_2014.pdf

accesso aperto

Descrizione: Arxiv
Tipologia: Pre-print (manoscritto inviato all'editore)
Dimensione 385.47 kB
Formato Adobe PDF
385.47 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/239990
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 13
  • ???jsp.display-item.citation.isi??? 16
social impact