Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions
Publication
, Journal Article
Liu, JG; Xu, X
Published in: SIAM Journal on Mathematical Analysis
January 1, 2017
In this paper we are concerned with the existence of a weak solution to the initial boundary value problem for the equation ∂u/∂t = Δ(Δu)-3. This problem arises in the mathematical modeling of the evolution of a crystal surface. Existence of a weak solution u with Δu ≥ 0 is obtained via a suitable substitution. Our investigations reveal the close connection between this problem and the equation ∂tρ+ρ2Δ2ρ3 = 0, another crystal surface model first proposed by H. Al Hajj Shehadeh, R. V. Kohn, and J. Weare [Phys. D, 240 (2011), pp. 1771-1784].
Duke Scholars
Published In
SIAM Journal on Mathematical Analysis
DOI
EISSN
1095-7154
ISSN
0036-1410
Publication Date
January 1, 2017
Volume
49
Issue
3
Start / End Page
2220 / 2245
Related Subject Headings
- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Liu, J. G., & Xu, X. (2017). Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions. SIAM Journal on Mathematical Analysis, 49(3), 2220–2245. https://doi.org/10.1137/16M1098474
Liu, J. G., and X. Xu. “Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions.” SIAM Journal on Mathematical Analysis 49, no. 3 (January 1, 2017): 2220–45. https://doi.org/10.1137/16M1098474.
Liu JG, Xu X. Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions. SIAM Journal on Mathematical Analysis. 2017 Jan 1;49(3):2220–45.
Liu, J. G., and X. Xu. “Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions.” SIAM Journal on Mathematical Analysis, vol. 49, no. 3, Jan. 2017, pp. 2220–45. Scopus, doi:10.1137/16M1098474.
Liu JG, Xu X. Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions. SIAM Journal on Mathematical Analysis. 2017 Jan 1;49(3):2220–2245.
Published In
SIAM Journal on Mathematical Analysis
DOI
EISSN
1095-7154
ISSN
0036-1410
Publication Date
January 1, 2017
Volume
49
Issue
3
Start / End Page
2220 / 2245
Related Subject Headings
- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics