Well-posedness for a class of abstract nonlinear parabolic systems with time delay

Nonlinear Analysis, Theory, Methods and Applications

Volumn 35, Issue 5, 1999, Pages 629-648

  Banks, H T ^a   Musante, C J ^a  

^a Center for Research in Scientific Computation   (United States)

Author keywords

Existence; Liver transport models; Nonlinear parabolic distributed parameter systems with delays; Toxicokinetic modeling; Uniqueness; Variational form

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; DISTRIBUTED PARAMETER CONTROL SYSTEMS; MATHEMATICAL MODELS; NONLINEAR CONTROL SYSTEMS; PARAMETER ESTIMATION; TOXICITY; VARIATIONAL TECHNIQUES;

CONVECTION-DISPERSION MODELS; NONLINEAR PARABOLIC MODELS;

NONLINEAR EQUATIONS;

EID: 0033101936     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00053-4     Document Type: Article

References (16)

1. Banks H.T., Gilliam D.S., Shubov V.L. Global solvability for damped abstract nonlinear hyperbolic systems. Differential and Integral Equations. 10:1997;309-332.
2. H.T. Banks, K. Ito, Y. Wang, Well-posedness for damped second order systems with unbounded input operators, CRSC-TR93-10, June 1993; Differential and Integral Equations 8 (1995) 587-606.
3. H.T. Banks, C.J. Musante, H.T. Tran, A dispersion model for the hepatic uptake and elimination of 2,3,7,8 -tetrachlorodibenzo- p -dioxin, CRSC-TR97-29, September, 1997; Math. Comput. Modelling, submitted.
4. H.T. Banks, R.C. Smith, Y. Wang, Smart Material Structures: Modeling Estimation, and Control, Wiley, New York, 1996 .
5. R. Bellman, K.L. Cooke, Differential-Difference Equations, Rand Corporation, 1963 .
6. Birnbaum L.S. The mechanism of dioxin toxicity: relationship to risk assessment. Environ. Health Perspect. 102:1994;157-167.
7. Henriksen G.L., Ketchum N.S., Michaelek J.E., Swaby J.A. Serum dioxin and diabetes mellitus in veterans of Operation Ranch Hand. Epidemiology. 8(3):1997;252-258.
8. Naylor A.W., Sell G.R. Linear Operator Theory in Engineering and Science. 1982;Springer, New York.
9. Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. 1983;Springer, New York.
10. Poland A., Glover E. Stereospecific, high affinity binding of. 2,3,7,8 -tetrachlorodibenzo- p -dioxin by hepatic cytosol J. Biol. Chem. 251:1976;4936-4946.
11. 125 I] 2-Iodo- 3,7,8 -trichlorodibenzo- p -dioxin-binding species in mouse liver induced by agonists for the Ah receptor: characterization and identification, Mol. Pharmacol. 36 (1989) 113-120.
12. Roberts M.S., Rowland M. A dispersion model of hepatic elimination: 1. Formulation of the model and bolus considerations. J. Pharmacokinet. Biopharm. 14:1986;227-260.
13. S.A. Skene, I.C. Dewhurst, M. Greenberg, Polychlorinated dibenzo- p -dioxins and polychlorinated dibenzofurans: the risks to human health, a review, Hum. Toxicol. 8 (1989) 173-203.
14. M. Van den Berg, J. De Jongh, H. Poiger, J. Olson, The toxicokinetics and metabolism of polychlorinated dibenzo- p -dioxins (PCDDs) and dibenzofurans (PCDFs) and their elevance for toxicity, Crit. Rev. Toxicol. 24 (1994) 1-74.
15. Voorman R., Aust S.D. Specific binding of polyhalogenated aromatic hydrocarbon inducers of cytochrome P-450d to the cytochrome and inhibition of its estradiol-2-hydroxylase activity. Toxicol. Appl. Pharmacol. 90:1987;69-78.
16. J. Wloka, Partial Differential Equations, Cambridge University Press, Cambridge, 1992 .