Optimization of crystal growth with diffusion
Author:
Gustaf Gripenberg
Journal:
Quart. Appl. Math. 40 (1982), 297-310
MSC:
Primary 49A34; Secondary 35K05, 35R35, 45D05
DOI:
https://doi.org/10.1090/qam/678201
MathSciNet review:
678201
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Abstract: A crystal growth process involving diffusion in a half-space is studied. Both the diffusion coefficient and the interface reaction term are assumed to depend on a control parameter that is (e.g.) a function of temperature. The thickness of the deposited film after a given time or the time to reach a certain thickness is to be optimized. The full Stefan problem is not considered and the diffusion coefficient is assumed to vary slowly with the parameter.
. R. Ghez and J. S. Lew, Interface kinetics and crystal growth under conditions of constant cooling rate, J. Crystal Growth 20, 273–282 (1973)
- Gustaf Gripenberg, On positive, nonincreasing resolvents of Volterra equations, J. Differential Equations 30 (1978), no. 3, 380–390. MR 521860, DOI https://doi.org/10.1016/0022-0396%2878%2990007-4
G. Gripenberg, On Volterra equations with nonconvolution kernels, Report-HTKK-MAT-A118, Helsinki University of Technology, 1978
- Gustaf Gripenberg, On the resolvents of nonconvolution Volterra kernels, Funkcial. Ekvac. 23 (1980), no. 1, 83–95. MR 586277
- Gustaf Gripenberg, Asymptotic solutions of some nonlinear Volterra integral equations, SIAM J. Math. Anal. 12 (1981), no. 4, 595–602. MR 617718, DOI https://doi.org/10.1137/0512052
- A. Halanay, Optimal controls for systems with time lag, SIAM J. Control 6 (1968), 215–234. MR 0247556
- R. K. Miller, J. A. Nohel, and J. S. W. Wong, Perturbations of Volterra integral equations, J. Math. Anal. Appl. 25 (1969), 676–691. MR 240573, DOI https://doi.org/10.1016/0022-247X%2869%2990265-0
H. Müller-Krumbhaar, Diffusion theory for crystal growth at arbitrary solute concentration, J. Chem. Phys. 63, 5131–5138 (1975)
- W. E. Olmstead, Diffusion systems reacting at the boundary, Quart. Appl. Math. 38 (1980/81), no. 1, 51–59. MR 575832, DOI https://doi.org/10.1090/S0033-569X-1980-0575832-6
- Walter Rudin, Functional analysis, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. McGraw-Hill Series in Higher Mathematics. MR 0365062
. R. Ghez and J. S. Lew, Interface kinetics and crystal growth under conditions of constant cooling rate, J. Crystal Growth 20, 273–282 (1973)
G. Gripenberg, On positive nonincreasing resolvents of Volterra equations, J. Differential Equations 30, 380–390 (1978)
G. Gripenberg, On Volterra equations with nonconvolution kernels, Report-HTKK-MAT-A118, Helsinki University of Technology, 1978
G. Gripenberg, On the resolvents of nonconvolution Volterra kernels, Funkcial. Ekvac. 23, 83–85 (1980)
G. Gripenberg, Asymptotic solutions of some nonlinear Volterra integral equations, SIAM J. Math. Anal. 12, 595–602 (1981)
A. Halanay, Optimal controls for systems with time lag, SIAM J. Control Optim. 6, 215–234 (1968)
R. K. Miller, J. A. Nohel and J. S. W. Wong, Perturbations of Volterra integral equations, J. Math. Anal. Appl. 25, 676–691 (1969)
H. Müller-Krumbhaar, Diffusion theory for crystal growth at arbitrary solute concentration, J. Chem. Phys. 63, 5131–5138 (1975)
W. E. Olmstead, Diffusion systems reacting at the boundary, Quart. Appl. Math. 38, 51–59 (1980)
W. Rudin, Functional analysis, McGraw-Hill, New York, 1973
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Article copyright:
© Copyright 1982
American Mathematical Society
