A linear integro-differential equation for viscoelastic rods and plates

Author:
Kenneth B. Hannsgen

Journal:
Quart. Appl. Math. **41** (1983), 75-83

MSC:
Primary 45K05; Secondary 73F99

DOI:
https://doi.org/10.1090/qam/700662

MathSciNet review:
700662

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Abstract: It is proved that the resolvent kernel of a certain integrodifferential equation in Hilbert space is absolutely integrable on . The equation arises in the linear theory of isotropic viscoelastic rods and plates.

**[1]**D. R. Bland,*The theory of linear viscoelasticity*, Pergamon Press, New York, 1960 MR**0110314****[2]**R. W. Carr and K. B. Hannsgen,*A nonhomogeneous integrodifferential equation in Hilbert space*, SIAM J. Math. Anal.**10**, 961-984 (1979) MR**541094****[3]**R. W. Carr and K. B. Hannsgen,*Resolvent formulas for a Volterra equation in Hilbert space*, SIAM J. Math. Anal.,**13**, 459-483 (1982). MR**653467****[4]**K. B. Hannsgen,*Indirect abelian theorems and a linear Volterra equation*, Trans. Amer. Math. Soc.**142**, 539-555 (1969) MR**0246058****[5]**K. B. Hannsgen,*Uniform L behavior for an integrodifferential equation with parameter*, SIAM J. Math. Anal.**8**, 626-639 (1977) MR**0463848****[6]**J. A. Nohel and D. F. Shea,*Frequency domain methods for Volterra equations*, Advances in Math.**22**, 278-304 (1976) MR**0500024****[7]**A. C. Pipkin,*Lectures on viscoelasticity theory*, Springer-Verlag, Heidelberg, 1972**[8]**D. F. Shea and S. Wainger,*Variants of the Wiener-Lévy theorem, with applications to stability problems for some Volterra integral equations*, Amer. J. Math.**97**, 312-343 (1975) MR**0372521**

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Additional Information

DOI:
https://doi.org/10.1090/qam/700662

Article copyright:
© Copyright 1983
American Mathematical Society