Continuous data dependence for an abstract Volterra integro-differential equation in Hilbert space with applications to viscoelasticity

Frederick Bloom

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1977)

  • Volume: 4, Issue: 1, page 179-207
  • ISSN: 0391-173X

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Bloom, Frederick. "Continuous data dependence for an abstract Volterra integro-differential equation in Hilbert space with applications to viscoelasticity." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 4.1 (1977): 179-207. <http://eudml.org/doc/83743>.

@article{Bloom1977,
author = {Bloom, Frederick},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {1},
pages = {179-207},
publisher = {Scuola normale superiore},
title = {Continuous data dependence for an abstract Volterra integro-differential equation in Hilbert space with applications to viscoelasticity},
url = {http://eudml.org/doc/83743},
volume = {4},
year = {1977},
}

TY - JOUR
AU - Bloom, Frederick
TI - Continuous data dependence for an abstract Volterra integro-differential equation in Hilbert space with applications to viscoelasticity
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1977
PB - Scuola normale superiore
VL - 4
IS - 1
SP - 179
EP - 207
LA - eng
UR - http://eudml.org/doc/83743
ER -

References

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  1. [1] C.M. Dafermos, An Abstract Volterra Equation with Applications to Linear Viscoelasticity, J. Diff. Eqs., 7 (1970), pp. 554-569. Zbl0212.45302MR259670
  2. [2] R.J. Knops - L.E. Payne, Growth Estimates for Solutions of Evolutionary equations in Hilbert Space with Applications in Elastodynamics, Arch. Rat. Mech. Anal., 41 (1971), pp. 369-398. Zbl0227.35017MR330731
  3. [3] R.J. Knops - L.E. Payne, Uniqueness in Classical Elastodynamics, Arch. Rat. Mech. Anal., 32 (1968), pp. 349-355. Zbl0159.56201MR219261
  4. [4] R.J. Knops - L.E. Payne, On Uniqueness and Continuous Dependence in Dynamical Problems of Linear Thermoelasticity, Int. J. Solids Structures, 6 (1969), pp. 1173-1184. Zbl0209.56605
  5. [5] H.A. Levine, Logarithmic Convexity and the Cauchy Problem for some Abstract Second Order Differential Inequalities, J. Diff. Eqs., 8 (1970), pp. 34-55. Zbl0194.13101MR259303
  6. [6] H.A. Levine, Uniqueness and Growth of Weak Solutions to certain Linear Differential Equations in Hilbert Space, J. Diff. Eqs., 17 (1975), pp. 73-81. Zbl0294.34044MR358014
  7. [7] C.E. Beevers, Uniqueness and Stability in Linear Viscoelasticity, ZAMP, 26 (1975), pp. 177-186. Zbl0314.73035MR366154
  8. [8] C.E. Beevers, Some Continuous Dependence Results in the Linear Dynamic Theory of Anisotropic Viscoelasticity, Journal de Mécanique, 14 (1975), pp. 1-13. Zbl0324.73031MR386404
  9. [9] A.C. Murray - M.H. Protter, The Asymptotic Behavior of Solutions of Second Order Systems of Partial Differential Equations, J. Diff . Eqs., 13 (1973), pp. 57-80. Zbl0257.35017MR328291
  10. [10] R.J. Knops - L.E. Payne, Continuous Data Dependence for the Equations of Classical Elastodynamics, Proc. Camb. Phil. Soc., 66 (1969), pp. 481-491. Zbl0184.51004MR270604
  11. [11] F. Bloom, Continuous Dependence on Initial Geometry for a Class of Abstract Equations in Hilbert Space, to appear in the J. Math. Anal. Appl. Zbl0347.35024MR442401
  12. [12] W.A. Day, On the Monotonicity of the Relaxation Functions of Viscoelastic Materials, Proc. Camb. Phil. Soc., 67 (1970), pp. 503-508. Zbl0202.25302MR250545
  13. [13] F. Bloom, On Stability in Linear Viscoelasticity, Mechanics Research Communications, 3 (1976), pp. 143-150. Zbl0367.73051
  14. [14] F. Bloom, Growth Estimates for Solutions to Initial-Boundary Value Problems in Viscoelasticity, to appear in the J. Math. Anal. Appl. Zbl0361.45010
  15. [15] F. Bloom, Stability and Growth Estimates for Volterra Integrodifferential Equations in Hilbert Space, Bull. A.M.S., 82 (1976), # 5. Zbl0329.45016

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