The stability of vector renewal equations pertaining to heterogeneous chemical reaction systems
Authors:
A. E. DeGance and L. E. Johns
Journal:
Quart. Appl. Math. 34 (1976), 69-83
MSC:
Primary 82.45
DOI:
https://doi.org/10.1090/qam/449376
MathSciNet review:
449376
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: For a class of vector renewal equations arising in the theory of spatially nonuniform chemical reaction processes, stability conditions are given in terms of the physicochemical operators D and K. In particular, we provide conditions for the stability of an initially uniform, multicomponent film bounding a planar catalytic surface, and for the asymptotic stability of a reaction system composed of a population of catalyst particles. We obtain such results by identifying a sup norm which is naturally induced from the factors that symmetrize D and/or K. Further, we exhibit conditions under which a special class of vector renewal equations has positive solutions.
- Richard Bellman, Introduction to matrix analysis, 2nd ed., McGraw-Hill Book Co., New York-Düsseldorf-London, 1970 (Russian). MR 0258847
- Richard Bellman and Kenneth L. Cooke, Differential-difference equations, Academic Press, New York-London, 1963. MR 0147745
A. E. DeGance, Diffusion—heterogeneous chemical reaction interference in multicomponent systems, Ph.D. dissertation, University of Florida, 1974
A. E. DeGance and L. E. Johns, The sensitivity of the selectivity to transport parameters in batch heterogeneous chemical reaction systems, Chem. Eng. J. 7, 227–244 (1974)
- Rodney D. Driver, Some harmless delays, Delay and functional differential equations and their applications (Proc. Conf., Park City, Utah, 1972) Academic Press, New York, 1972, pp. 103–119. MR 0385277
- R. J. Duffin, A minimax theory for overdamped networks, J. Rational Mech. Anal. 4 (1955), 221–233. MR 69030, DOI https://doi.org/10.1512/iumj.1955.4.54007
Handbook of mathematical functions, N. B. S. AMS 55, Government Printing Office, Wạashington, D. C., 1965
J. L. Hudson, Transient multicomponent diffusion with heterogeneous reaction, A.I.Ch.E. J. 13, 961–964 (1967)
L. E. Johns and X. B. Reed, Diffusion—heterogeneous chemical reaction in multicomponent systems. I. The penetration theory for single catalyst particles in a dilute turbulent suspension, Chem. Engng. Sci. 28, 275–288 (1973)
L. E. Johns and X. B. Reed, On imperfect contacting in batch heterogeneous chemical reaction systems, Chem. Engng. Sci. 28, 1591–1609 (1973)
- Richard K. Miller, Nonlinear Volterra integral equations, W. A. Benjamin, Inc., Menlo Park, Calif., 1971. Mathematics Lecture Note Series. MR 0511193
- J. A. Nohel, Some problems in nonlinear Volterra integral equations, Bull. Amer. Math. Soc. 68 (1962), 323–329. MR 145307, DOI https://doi.org/10.1090/S0002-9904-1962-10790-3
- Georgi E. Shilov, An introduction to the theory of linear spaces, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1961. Translated from the Russian by Richard A. Silverman. MR 0126450
R. Bellman, Introduction to matrix analysis, McGraw-Hill, New York, 1970
R. Bellman and K. L. Cooke, Differential-difference equations, Academic Press, New York, 1963
A. E. DeGance, Diffusion—heterogeneous chemical reaction interference in multicomponent systems, Ph.D. dissertation, University of Florida, 1974
A. E. DeGance and L. E. Johns, The sensitivity of the selectivity to transport parameters in batch heterogeneous chemical reaction systems, Chem. Eng. J. 7, 227–244 (1974)
R. Driver, Some harmless delays, pp. 103–119 in Delay and functional differential equations and their applications (ed. K. Schmitt), Academic Press, New York, 1972
R. J. Duffin, A minimal theory for overdamped networks, J. Rat. Mech. and Analysis 4, 221–233 (1955)
Handbook of mathematical functions, N. B. S. AMS 55, Government Printing Office, Wạashington, D. C., 1965
J. L. Hudson, Transient multicomponent diffusion with heterogeneous reaction, A.I.Ch.E. J. 13, 961–964 (1967)
L. E. Johns and X. B. Reed, Diffusion—heterogeneous chemical reaction in multicomponent systems. I. The penetration theory for single catalyst particles in a dilute turbulent suspension, Chem. Engng. Sci. 28, 275–288 (1973)
L. E. Johns and X. B. Reed, On imperfect contacting in batch heterogeneous chemical reaction systems, Chem. Engng. Sci. 28, 1591–1609 (1973)
R. K. Miller, Nonlinear Volterra integral equations, Benjamin, Menlo Park, 1971
J. A. Nohel, Some problems in nonlinear Volterra integral equations, Bull. Amer. Math. Soc. 68, 323–329 (1962)
G. E. Shilov, An introduction to the theory of linear spaces, Prentice-Hall, Englewood Cliffs, 1961
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
82.45
Retrieve articles in all journals
with MSC:
82.45
Additional Information
Article copyright:
© Copyright 1976
American Mathematical Society
