The extent of spatial regularity for parabolic integrodifferential equations

  • Ronald Grimmer
  • Eugenio Sinestrari
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1223)


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  1. 1.
    P. L. Butzer and H. Berens, Semi-Groups of Operators and Approximation, Springer-Verlag, New York, 1967.CrossRefzbMATHGoogle Scholar
  2. 2.
    G. DaPrato and M. Iannelli, Existence and regularity for a class of integrodifferential equations of parabolic type, to appear J. Math. Anal. Appl.Google Scholar
  3. 3.
    G. DaPrato and M. Iannelli, Linear integrodifferential equations in Banach spaces, Rend. Sem. Mat. Padova, 62(1980), 207–219.MathSciNetGoogle Scholar
  4. 4.
    W. Desch, R. Grimmer and W. Schappacher, Some considerations for linear integrodifferential equations, J. Math. Anal. Appl., 104(1984), 219–234.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    A. Friedman and M. Shinbrot, Volterra integral equations in Banach space, Trans. Amer. Math. Soc., 126(1967), 131–179.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    R. Grimmer and F. Kappel, Series expansions for resolvents of Volterra integrodifferential equations in Banach spaces, SIAM J. Math. Anal., 15(1984), 595–604.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    R. Grimmer and A. J. Pritchard, Analytic resolvent operators for integral equations in Banach space, J. Diff. Eq., 50(1983), 234–259.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    R. Grimmer and J. Prüss, On linear Volterra equations in Banach spaces, Special Issue on Hyperbolic Partial Differential Equations, Comp. Math. Appl. to appear.Google Scholar
  9. 9.
    K. B. Hannsgen and R. L. Wheeler, Behavior of the solution of a Volterra equation as a parameter tends to infinity, J. Integral Eq., 7(1984), 229–238.MathSciNetzbMATHGoogle Scholar
  10. 10.
    D. D. Joseph, M. Renardy and J. Saut, Hyperbolicity and change of type in the flow of viscoelastic fluids, MRC Technical Summary Report #2657, Madison, Wisconsin, 1984.Google Scholar
  11. 11.
    A. Narain and D. D. Joseph, Remarks about the interpretation of impulse experiments in shear flows of viscoelastic liquids, Rheol. Acta 22(1983), 528–538.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    M. Renardy, Some remarks on the propagation and non-propagation of discontinuities in linearly viscoelastic liquids, Rheol. Acta 21(1982), 251–254.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Ronald Grimmer
    • 1
  • Eugenio Sinestrari
    • 2
  1. 1.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA
  2. 2.Dipartimento di MatematicaUniversità di RomaRomaItaly

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