×
Grimmer, R. C.

Resolvent operators for integral equations in a Banach space. (English) Zbl 0493.45015

Trans. Am. Math. Soc. 273, 333-349 (1982).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0493.45015

Cited in 30 Reviews
Cited in 156 Documents

MSC:

45N05 Abstract integral equations, integral equations in abstract spaces
45J05 Integro-ordinary differential equations
45D05 Volterra integral equations
45M05 Asymptotics of solutions to integral equations

Keywords:

weak solutions; resolvent operators; Banach space; evolution equation; asymptotic behavior
PDF BibTeX XML Cite
\textit{R. C. Grimmer}, Trans. Am. Math. Soc. 273, 333--349 (1982; Zbl 0493.45015)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Goong Chen, Control and stabilization for the wave equation in a bounded domain, SIAM J. Control Optim. 17 (1979), no. 1, 66 – 81. · Zbl 0402.93016
[2] Goong Chen and Ronald Grimmer, Semigroups and integral equations, J. Integral Equations 2 (1980), no. 2, 133 – 154. · Zbl 0449.45007
[3] -, Integral equations as evolution equations, J. Differential Equations (to appear). · Zbl 0449.45008
[4] Avner Friedman and Marvin Shinbrot, Volterra integral equations in Banach space, Trans. Amer. Math. Soc. 126 (1967), 131 – 179. · Zbl 0147.12302
[5] R. C. Grimmer and R. K. Miller, Existence, uniqueness, and continuity for integral equations in a Banach space, J. Math. Anal. Appl. 57 (1977), no. 2, 429 – 447. · Zbl 0354.45006
[6] R. C. Grimmer and R. K. Miller, Well-posedness of Volterra integral equations in Hilbert space, J. Integral Equations 1 (1979), no. 3, 201 – 216. · Zbl 0462.45020
[7] Ronald Grimmer and George Seifert, Stability properties of Volterra integrodifferential equations, J. Differential Equations 19 (1975), no. 1, 142 – 166. · Zbl 0321.45017
[8] S. I. Grossman and R. K. Miller, Perturbation theory for Volterra integrodifferential systems, J. Differential Equations 8 (1970), 457 – 474. · Zbl 0209.14101
[9] Morton E. Gurtin and A. C. Pipkin, A general theory of heat conduction with finite wave speeds, Arch. Rational Mech. Anal. 31 (1968), no. 2, 113 – 126. · Zbl 0164.12901
[10] Kenneth B. Hannsgen, The resolvent kernel of an integrodifferential equation in Hilbert space, SIAM J. Math. Anal. 7 (1976), no. 4, 481 – 490. · Zbl 0334.45004
[11] Kenneth B. Hannsgen, Uniform \?\textonesuperior behavior for an integrodifferential equation with parameter, SIAM J. Math. Anal. 8 (1977), no. 4, 626 – 639. · Zbl 0357.45007
[12] Tosio Kato, Linear evolution equations of ”hyperbolic” type, J. Fac. Sci. Univ. Tokyo Sect. I 17 (1970), 241 – 258. · Zbl 0222.47011
[13] Tosio Kato, Linear evolution equations of ”hyperbolic” type. II, J. Math. Soc. Japan 25 (1973), 648 – 666. · Zbl 0262.34048
[14] Richard K. Miller, Volterra integral equations in a Banach space, Funkcial. Ekvac. 18 (1975), no. 2, 163 – 193. · Zbl 0326.45007
[15] R. K. Miller, An integro-differential equation for rigid heat conductors with memory, J. Math. Anal. Appl. 66 (1978), no. 2, 313 – 332. · Zbl 0391.45012
[16] Richard K. Miller, Nonlinear Volterra integral equations, W. A. Benjamin, Inc., Menlo Park, Calif., 1971. Mathematics Lecture Note Series. · Zbl 0448.45004
[17] Richard K. Miller and Robert L. Wheeler, Asymptotic behavior for a linear Volterra integral equation in Hilbert space, J. Differential Equations 23 (1977), no. 2, 270 – 284. · Zbl 0341.45017
[18] Richard K. Miller and Robert L. Wheeler, Well-posedness and stability of linear Volterra integro-differential equations in abstract spaces, Funkcial. Ekvac. 21 (1978), no. 3, 279 – 305. · Zbl 0399.45021
[19] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Dept. Math. Lecture Note # 10, University of Maryland, 1974. · Zbl 0516.47023
[20] A. J. Pritchard and J. Zabczyk, Stability and stabilizability of infinite-dimensional systems, SIAM Rev. 23 (1981), no. 1, 25 – 52. · Zbl 0452.93029
[21] Hiroki Tanabe, Equations of evolution, Monographs and Studies in Mathematics, vol. 6, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1979. Translated from the Japanese by N. Mugibayashi and H. Haneda. · Zbl 0417.35003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.