 Theoretical and numerical study of the Landau-Khalatnikov model describing a formation of 2D domain patterns in ferroelectricsA.G. Maslovskaya, E.M. Veselova, A.Yu. Chebotarev and A.E. Kovtanyuk Applied Mathematics and Computation, 2024, vol. 466, issue C Abstract: Among the numerous applications of the Ginzburg-Landau theory to the analysis of significant reaction-diffusion systems, modeling of the behavior of promising polar dielectric materials should be especially highlighted. The paper is devoted to the theoretical and numerical analysis of the Landau-Khalatnikov model describing the dynamics of 2D domain pattern formation in ferroelectrics. The unique solvability of the initial-boundary value problem for the system of 2D cubic-quintic Landau-Khalatnikov equations is proved. The proof is based on the derivation of new a priori estimates for the solution of the system of nonlinear parabolic equations. A series of computational experiments are conducted to examine both spontaneous and polar-induced domain pattern formation in biaxial ferroelectrics. Finite-element simulations allow us to visualize different types of ferroelectric domain structures depending on the varying boundary conditions. Keywords: Landau-Ginzburg-Devonshire theory; Landau-Khalatnikov equation; Reaction-diffusion model; A priori estimates; Unique solvability; Ferroelectric domain pattern (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:466:y:2024:i:c:s0096300323006409 DOI: 10.1016/j.amc.2023.128471 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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