References
- Guiochon G, Lin B. Modeling for preparative chromatography. New York (NY): Academic Press; 2003.
- Seidel-Morgenstern A. Experimental determination of single solute and competitive adsorption isotherms. J Chromatogr A. 2004;1037(1):255–272.
- Lindholm J, Forssén P, Fornstedt T. Validation of the accuracy of the perturbation peak method for determination of single and binary adsorption isotherm parameters in lc. Anal Chem. 2004;76(16):4856–4865.
- Lisec O, Hugo P, Seidel-Morgenstern A. Frontal analysis method to determine competitive adsorption isotherms. J Chromatogr A. 2001;908(1–2):19–34.
- Dose EV, Jacobson S, Guiochon G. Determination of isotherms from chromatographic peak shapes. Anal Chem. 1991;63(8):833–839.
- Felinger A, Zhou D, Guiochon G. Determination of the single component and competitive adsorption isotherms of the 1-indanol enantiomers by the inverse method. J Chromatogr A. 2003;1005(1–2):35–49.
- Forssén P, Fornstedt T. A model free method for estimation of complicated adsorption isotherms in liquid chromatography. J Chromatogr A. 2015;1409:108–115.
- Forssén P, Arnell R, Fornstedt T. An improved algorithm for solving inverse problems in liquid chromatography. Comput Chem Eng. 2006;30(9):1381–1391.
- Zhang Y, Lin G, Forssén P, et al. A regularization method for the reconstruction of adsorption isotherms in liquid chromatography. Inverse Prob. 2016;32(10):105005.
- Kohn R, Vogelius M. Determining conductivity by boundary measurements. Commun Pure Appl Math. 1984;37(3):289–298.
- Afraites L, Dambrine M, Kateb D. Conformal mappings and shape derivatives for the transmission problem with a single measurement. HAL. 2006. Preprint.
- Zhang Y, Lin G, Gulliksson M, et al. An adjoint method in inverse problems of chromatography. Inverse Prob Sci Eng. 2016. DOI:10.1080/17415977.2016.1222528.
- Guiochon G, Shirazi G, Katti M. Fundamentals of preparative and nonlinear chromatography. 2nd ed. Netherlands: Elsevier; 2006.
- Gritti F, Guiochon G. Characteristics of the adsorption mechanism of acido-basic compounds with two pka in reversed-phase liquid chromatography. J Chromatogr A. 2009;1216(41):6917–6930.
- Rudin W. Functional analysis. 2nd ed. New York (NY): McGraw-Hill Science; 1991.
- Ladyzhenskaya O, Solonnikov V, Uraltseva N. Linear and quasi-linear equations of parabolic type. London: American Mathematical Society; 1991.
- Lieberman G. Second order parabolic differential equations. London: World Scientific Publishing; 2005.
- Kvaalen E, Neel L, Tondeur D. Directions of quasi-static mass and energy transfer between phases in multicomponent open systems: Implications in separation science. Chem Eng Technol. 1985;40(7):1191–1204.
- Schock E. Approximate solution of ill-posed equations: arbitrarily slow convergence vs. superconvergence. Vol. 73, Constructive methods for the practical treatment of integral equations. 1985. p. 234–243.
- Vogel C. Computational methods for inverse problems. Philadelphia: SIAM; 2002.
- Engl H, Hanke M, Neubauer A. Regularization of inverse problems. Dordrecht: Kluwer; 1996.
- Kügler P. Identification of a temperature dependent heat conductivity from single boundary measurements. SIAM J Numer Anal. 2003;41(4):1543–1563.
- Arkhipova A. On the partial regularity up to the boundary of weak solutions to quasilinear parabolic systems with quadratic growth. Zap Nauchn Sem POMI. 1997;249:20–39.
- Anzengruber SW, Ramlau R. Morozov’s discrepancy principle for tikhonov-type functionals with nonlinear operators. Inverse Prob. 2010;26(2):25001–25017(17).
- Nocedal J, Wright SJ. Numerical optimization. 2nd ed. New York (NY): Springer; 2006.
- Fiacco AV. Introduction to sensitivity and stability analysis in nonlinear programming. New York (NY): Academic press; 1983.