A vicinal surface model for epitaxial growth with logarithmic free energy
Publication
, Journal Article
Gao, Y; Ji, H; Liu, JG; Witelski, TP
Published in: Discrete and Continuous Dynamical Systems - Series B
December 1, 2018
We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulting nonlinear partial differential equation, ut = -u2(u3 + au)hhhh, gives the evolution for the surface slope u as a function of the local height h in a monotone step train. Subject to periodic boundary conditions and positive initial conditions, we prove the existence, uniqueness and positivity of global strong solutions to this PDE using two Lyapunov energy functions. The long time behavior of u converging to a constant that only depends on the initial data is also investigated both analytically and numerically.
Duke Scholars
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Published In
Discrete and Continuous Dynamical Systems - Series B
DOI
ISSN
1531-3492
Publication Date
December 1, 2018
Volume
23
Issue
10
Start / End Page
4433 / 4453
Related Subject Headings
- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
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Gao, Y., Ji, H., Liu, J. G., & Witelski, T. P. (2018). A vicinal surface model for epitaxial growth with logarithmic free energy. Discrete and Continuous Dynamical Systems - Series B, 23(10), 4433–4453. https://doi.org/10.3934/dcdsb.2018170
Gao, Y., H. Ji, J. G. Liu, and T. P. Witelski. “A vicinal surface model for epitaxial growth with logarithmic free energy.” Discrete and Continuous Dynamical Systems - Series B 23, no. 10 (December 1, 2018): 4433–53. https://doi.org/10.3934/dcdsb.2018170.
Gao Y, Ji H, Liu JG, Witelski TP. A vicinal surface model for epitaxial growth with logarithmic free energy. Discrete and Continuous Dynamical Systems - Series B. 2018 Dec 1;23(10):4433–53.
Gao, Y., et al. “A vicinal surface model for epitaxial growth with logarithmic free energy.” Discrete and Continuous Dynamical Systems - Series B, vol. 23, no. 10, Dec. 2018, pp. 4433–53. Scopus, doi:10.3934/dcdsb.2018170.
Gao Y, Ji H, Liu JG, Witelski TP. A vicinal surface model for epitaxial growth with logarithmic free energy. Discrete and Continuous Dynamical Systems - Series B. 2018 Dec 1;23(10):4433–4453.
Published In
Discrete and Continuous Dynamical Systems - Series B
DOI
ISSN
1531-3492
Publication Date
December 1, 2018
Volume
23
Issue
10
Start / End Page
4433 / 4453
Related Subject Headings
- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics