Time discretization of an initial value problem for a simultaneous\n abstract evolution equation applying to parabolic-hyperbolic phase-field\n systems

2019/06/17 by Shunsuke Kurima, Kurima, Shunsuke
Engineering · Materials Science · Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Solidification and crystal growth phenomena #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1906.06887

openalex publication_date 2019/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article deals with a simultaneous abstract evolution equation. This\nincludes a parabolic-hyperbolic phase-field system as an example which consists\nof a parabolic equation for the relative temperature coupled with a semilinear\ndamped wave equation for the order parameter. Although a time discretization of\nan initial value problem for an abstract evolution equation has been studied,\ntime discretizations of initial value problems for simultaneous abstract\nevolution equations seem to be not studied yet. In this paper we focus on a\ntime discretization of a simultaneous abstract evolution equation applying to\nparabolic-hyperbolic phase-field systems. Moreover, we can establish an error\nestimate for the difference between continuous and discrete solutions.\n

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