2015/10/13 by Christian Heinemann, Heinemann, C., Christiane Kraus +5
Computer Science · Engineering · Materials Science · #35D30 #74A45 #74G25 #82B26 #93C55 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.1510.03755
openalex publication_date 2015/10/13 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
In this paper we study a model for phase separation and damage in\nthermoviscoelastic materials. The main novelty of the paper consists in the\nfact that, in contrast with previous works in the literature (cf., e.g., [C.\nHeinemann, C. Kraus: Existence results of weak solutions for Cahn-Hilliard\nsystems coupled with elasticity and damage. Adv. Math. Sci. Appl. 21 (2011),\n321--359] and [C. Heinemann, C. Kraus: Existence results for diffuse interface\nmodels describing phase separation and damage. European J. Appl. Math. 24\n(2013), 179--211]), we encompass in the model thermal processes, nonlinearly\ncoupled with the damage, concentration and displacement evolutions. More in\nparticular, we prove the existence of "entropic weak solutions", resorting to a\nsolvability concept first introduced in [E. Feireisl: Mathematical theory of\ncompressible, viscous, and heat conducting fluids. Comput. Math. Appl. 53\n(2007), 461--490] in the framework of Fourier-Navier-Stokes systems and then\nrecently employed in [E. Feireisl, H. Petzeltov 'a, E. Rocca: Existence of\nsolutions to a phase transition model with microscopic movements. Math. Methods\nAppl. Sci. 32 (2009), 1345--1369], [E. Rocca, R. Rossi: "Entropic" solutions to\na thermodynamically consistent PDE system for phase transitions and damage.\nSIAM J. Math. Anal., 47 (2015), 2519--2586] for the study of PDE systems for\nphase transition and damage. Our global-in-time existence result is obtained by\npassing to the limit in a carefully devised time-discretization scheme.\n