On the stability of an operator equation modeling nuclear reactors with delayed neutrons

Authors:
J. A. Walker and E. F. Infante

Journal:
Quart. Appl. Math. **34** (1977), 421-427

MSC:
Primary 82.45

DOI:
https://doi.org/10.1090/qam/446262

MathSciNet review:
446262

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References | Similar Articles | Additional Information

**[1]**W. Baran and K. Meyer,*Effect of delayed neutrons on the stability of a nuclear reactor*, Nuclear Sci. Engin.**24**, 356-361 (1966)**[2]**T. A. Bronikowski, J. E. Hall and J. A. Nohel,*Quantitative estimates for nonlinear systems of integrodifferential equations arising in reactor dynamics*, SIAM J. Math. Anal.**3**, 567-588 (1972) MR**0315378****[3]**M. G. Crandall and T. M. Liggett,*Generation of semigroups of nonlinear transformations on general Banach spaces*, Am. J. Math.**93**, 265-998 (1971) MR**0287357****[4]**E. F. Infante and J. A. Walker,*On the stability properties of an equation arising in reactor dynamics*, J. Math. Anal, and Appl.**55**, 112-124 (1976) MR**0408651****[5]**T. Kato,*Accretive operators and nonlinear evolution equations in Banach spaces*, in*Proc. Symp. in Pure Math*.**18**, Am. Math. Soc., Providence, R. I., pp. 138-161 (1970) MR**0271782****[6]**J. J. Levin and J. A. Nohel,*On a system of integrodifferential equations occurring in reactor dynamics*, J. Math. Mech.**9**, 347-368 (1960) MR**0117522****[7]**J. J. Levin and J. A. Nohel,*A system of nonlinear integrodifferential equations*, Michigan Math. J.**13**, 257-270 (1966) MR**0203421****[8]**J. J. Levin and J. A. Nohel,*A nonlinear system of integrodifferential equations*, in*Mathematical theory of control*, Academic Press, New York, pp. 398-405 (1967) MR**0253004****[9]**J. J. Levin and J. A. Nohel,*The integrodifferential equations of a class of nuclear reactors with delayed*neutrons, Arch. Rat. Mech. Anal.**31**, 151-171 (1968) MR**0236641****[10]**R. K. Miller,*On the linearization of Volterra integral equations*, J. Math. Anal. Appl.**23**, 198-203 (1968) MR**0230070****[11]**R. K. Miller,*An unstable nonlinear integrodifferential system*, in*Proceedings, U.S.-Japan Seminar on Differential and Functional Equations*, W. A. Benjamin, New York, pp. 479-489 (1967) MR**0240582****[12]**J. A. Nohel,*Some problems in nonlinear Volterra integral equations*, Bull. Amer. Math. Soc.**68**, 323-329 (1962) MR**0145307****[13]**R. S. Phillips,*Dissipative operators and hyperbolic systems of partial differential equations*, Trans. Am. Math. Soc.**90**, 193-254 (1959) MR**0104919****[14]**M. Slemrod,*A property of - semigroups*, unpublished note, Center for Dynamical Systems, Brown University, Providence, R. I. (1972)**[15]**A. Suhadolc,*On a system of integrodifferential equations*, SIAM J. Appl. Math.**21**, 195-206 (1971)**[16]**J. A. Walker,*On the application of Liapunov's Direct Method to linear dynamical systems*; J. Math. Anal. Appl.**53**, 187-220 (1976) MR**0410023****[17]**J. A. Walker and E. F. Infante,*Some results on the compactness of orbits of dynamical systems*, J. Math. Anal, and Appl.**51**, 56-67 (1975) MR**0393684**

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Additional Information

DOI:
https://doi.org/10.1090/qam/446262

Article copyright:
© Copyright 1977
American Mathematical Society