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Theoretical and numerical study of the Landau-Khalatnikov model describing a formation of 2D domain patterns in ferroelectrics

Author

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  • Maslovskaya, A.G.
  • Veselova, E.M.
  • Chebotarev, A.Yu.
  • Kovtanyuk, A.E.

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.

Suggested Citation

  • Maslovskaya, A.G. & Veselova, E.M. & Chebotarev, A.Yu. & Kovtanyuk, A.E., 2024. "Theoretical and numerical study of the Landau-Khalatnikov model describing a formation of 2D domain patterns in ferroelectrics," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    • Handle: RePEc:eee:apmaco:v:466:y:2024:i:c:s0096300323006409
    DOI: 10.1016/j.amc.2023.128471
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