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Optimal control of a diffusion/reaction/switching system
1. | Department of Mathematics and Statistics, University of Maryland Baltimore County (UMBC), Baltimore, MD 21250 |
References:
[1] |
T. C. Hazen, Cometabolic Bioremediation (Ch. 7, pp. 2505-2514) and In Situ Groundwater Bioremediation (Ch. 13, pp. 2583-2596) in Handbook of Hydrocarbon Lipid Microbiology, (Timmins et al., eds) Springer, NY, 2010. |
[2] |
M. A. Krasnosel'skĭi and A. V. Pokrovskiĭ, Systems with Hysteresis, Translated from the Russian by Marek Niezgódka. Springer-Verlag, Berlin, 1989.
doi: 10.1007/978-3-642-61302-9. |
[3] |
S. Lenhart, T. I. Seidman and J. Yong, Optimal control of a bioreactor with modal switching, Math. Models Methods in Appl. Sci., 11 (2001), 933-949.
doi: 10.1142/S0218202501001185. |
[4] |
R. D. Norris, et al., Handbook of Bioremediation, Lewis Publishers, Boca Raton, 1994. |
[5] |
T. I. Seidman, Switching systems: Thermostats and periodicity, Math. Res. Report 83-07, UMBC, 1983. http://userpages.umbc.edu/ seidman/ss_83.pdf |
[6] |
T. I. Seidman, A 1-dimensional bioremediation model with modal switching, in Control of Distributed Parameter and Stochastic Systems, (S. Chen, X. Li, J. Yong, X.Y. Zhou, eds.) pp. 127-131, Kluwer Acad. Publ., Norwell, 1999. |
[7] |
T. I. Seidman, A convection/reaction/switching system, Nonlinear Anal. - TMA, 67 (2007), 2060-2071.
doi: 10.1016/j.na.2006.08.050. |
[8] |
T. I. Seidman, Some aspects of modeling with discontinuities, Int'l. J. Evolution Eqns., 3 (2009), 419-433. |
[9] |
G. Stampacchia, Equations Elliptiques Du Second Ordre á Coefficients Discontinues, (French) Séminaire de Mathématiques Supérieures, No. 16 (été, 1965); Les Presses de l'Université de Montréal, Montreal, Que. 1966 326 pp. |
[10] |
E. Venkataramani and R. Ahlert, Role of cometabolism in biological oxidation of synthetic compounds, Biotechnology and Bioengineering, 27 (1985) 1306-1311.
doi: 10.1002/bit.260270906. |
[11] |
A. Visintin, Differential Models of Hysteresis, Applied Mathematical Sciences, 111. Springer-Verlag, Berlin, 1994. |
show all references
References:
[1] |
T. C. Hazen, Cometabolic Bioremediation (Ch. 7, pp. 2505-2514) and In Situ Groundwater Bioremediation (Ch. 13, pp. 2583-2596) in Handbook of Hydrocarbon Lipid Microbiology, (Timmins et al., eds) Springer, NY, 2010. |
[2] |
M. A. Krasnosel'skĭi and A. V. Pokrovskiĭ, Systems with Hysteresis, Translated from the Russian by Marek Niezgódka. Springer-Verlag, Berlin, 1989.
doi: 10.1007/978-3-642-61302-9. |
[3] |
S. Lenhart, T. I. Seidman and J. Yong, Optimal control of a bioreactor with modal switching, Math. Models Methods in Appl. Sci., 11 (2001), 933-949.
doi: 10.1142/S0218202501001185. |
[4] |
R. D. Norris, et al., Handbook of Bioremediation, Lewis Publishers, Boca Raton, 1994. |
[5] |
T. I. Seidman, Switching systems: Thermostats and periodicity, Math. Res. Report 83-07, UMBC, 1983. http://userpages.umbc.edu/ seidman/ss_83.pdf |
[6] |
T. I. Seidman, A 1-dimensional bioremediation model with modal switching, in Control of Distributed Parameter and Stochastic Systems, (S. Chen, X. Li, J. Yong, X.Y. Zhou, eds.) pp. 127-131, Kluwer Acad. Publ., Norwell, 1999. |
[7] |
T. I. Seidman, A convection/reaction/switching system, Nonlinear Anal. - TMA, 67 (2007), 2060-2071.
doi: 10.1016/j.na.2006.08.050. |
[8] |
T. I. Seidman, Some aspects of modeling with discontinuities, Int'l. J. Evolution Eqns., 3 (2009), 419-433. |
[9] |
G. Stampacchia, Equations Elliptiques Du Second Ordre á Coefficients Discontinues, (French) Séminaire de Mathématiques Supérieures, No. 16 (été, 1965); Les Presses de l'Université de Montréal, Montreal, Que. 1966 326 pp. |
[10] |
E. Venkataramani and R. Ahlert, Role of cometabolism in biological oxidation of synthetic compounds, Biotechnology and Bioengineering, 27 (1985) 1306-1311.
doi: 10.1002/bit.260270906. |
[11] |
A. Visintin, Differential Models of Hysteresis, Applied Mathematical Sciences, 111. Springer-Verlag, Berlin, 1994. |
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