2011/09/15 by Pierluigi Colli, Gianni Gilardi, Colli, Pierluigi +5
Computer Science · Engineering · Materials Science · #35A05 #35B40 #35K55 #74A15 #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.1109.3303
openalex publication_date 2011/09/15 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28
This paper is concerned with a diffusion model of phase-field type,\nconsisting of a parabolic system of two partial differential equations,\ninterpreted as balances of microforces and microenergy, for two unknowns: the\nproblem's order parameter and the chemical potential; each equation includes a\nviscosity term and the field equations are complemented by Neumann homogeneous\nboundary conditions and suitable initial conditions. In the recent paper\narXiv:1103.4585v1 [math.AP] we proved that this problem is well posed and\ninvestigated the long-time behavior of its solutions. Here we discuss the\nasymptotic limit of the system as the viscosity coefficient of the order\nparameter equation tends to 0. We prove convergence of solutions to the\ncorresponding solutions for the limit problem, whose long-time behavior we\ncharacterize; in the proofs, we employ compactness and monotonicity arguments.\n