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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**[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 a nonlinear system of integrodifferential equations arising in reactor dynamics*, SIAM J. Math. Anal.**3**(1972), 567–588. MR**0315378**, https://doi.org/10.1137/0503056**[3]**M. G. Crandall and T. M. Liggett,*Generation of semi-groups of nonlinear transformations on general Banach spaces*, Amer. J. Math.**93**(1971), 265–298. MR**0287357**, https://doi.org/10.2307/2373376**[4]**E. F. Infante and J. A. Walker,*On the stability properties of an equation arising in reactor dynamics*, J. Math. Anal. Appl.**55**(1976), no. 1, 112–124. MR**0408651**, https://doi.org/10.1016/0022-247X(76)90281-X**[5]**Tosio Kato,*Accretive operators and nonlinear evolution equations in Banach spaces.*, Nonlinear Functional Analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 1, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 138–161. MR**0271782****[6]**J. J. Levin and J. A. Nohel,*On a system of integro-differential equations occurring in reactor dynamics*, J. Math. Mech.**9**(1960), 347–368. MR**0117522****[7]**J. J. Levin and J. A. Nohel,*A system of nonlinear integrodifferential equations*, Michigan Math. J.**13**(1966), 257–270. MR**0203421****[8]**J. J. Levin and J. A. Nohel,*A nonlinear system of integrodifferential equations*, Mathematical Theory of Control (Proc. Conf., Los Angeles, Calif., 1967) Academic Press, New York, 1967, pp. 398–405. MR**0253004****[9]**J. J. Levin and J. A. Nohel,*The integrodifferential equations of a class of nuclear reactors with delayed neutrons*, Arch. Rational Mech. Anal.**31**(1968), 151–172. MR**0236641**, https://doi.org/10.1007/BF00281375**[10]**R. K. Miller,*On the linearization of Volterra integral equations*, J. Math. Anal. Appl.**23**(1968), 198–208. MR**0230070**, https://doi.org/10.1016/0022-247X(68)90127-3**[11]**R. K. Miller,*An unstable nonlinear integrodifferential system*, Proc. U.S.-Japan Seminar on Differential and Functional Equations (Minneapolis, Minn., 1967) Benjamin, New York, 1967, pp. 479–489. MR**0240582****[12]**J. A. Nohel,*Some problems in nonlinear Volterra integral equations*, Bull. Amer. Math. Soc.**68**(1962), 323–329. MR**0145307**, https://doi.org/10.1090/S0002-9904-1962-10790-3**[13]**R. S. Phillips,*Dissipative operators and hyperbolic systems of partial differential equations*, Trans. Amer. Math. Soc.**90**(1959), 193–254. MR**0104919**, https://doi.org/10.1090/S0002-9947-1959-0104919-1**[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**(1976), no. 2, 187–220. MR**0410023**, https://doi.org/10.1016/0022-247X(76)90104-9**[17]**J. A. Walker and E. F. Infante,*Some results on the precompactness of orbits of dynamical systems*, J. Math. Anal. Appl.**51**(1975), 56–67. MR**0393684**, https://doi.org/10.1016/0022-247X(75)90140-7

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Additional Information

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

Article copyright:
© Copyright 1977
American Mathematical Society