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Dynamic stability of one-dimensional nonlinearly viscoelastic bodies

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References

  • S.S. Antman (1972) The Theory of Rods, Handbuch der Physik, Vol. VIa/2, Springer-Verlag, Berlin-Heidelberg-New York.

    Google Scholar 

  • S.S. Antman (1976a) Ordinary Differential Equations of Non-Linear Elasticity I: Foundations of the Theories of Non-Linearly Elastic Rods and Shells, Arch. Rational Mech. Anal. 61, 307–351.

    Google Scholar 

  • S.S. Antman (1976b) Ordinary Differential Equations of Non-Linear Elasticity II: Existence and Regularity Theory for Conservative Boundary Value Problems, Arch. Rational Mech. Anal., 61, 353–393.

    Google Scholar 

  • R.C. Browne (1976) Dynamic Stability of One-Dimensional Non-Linearly Visco-Elastic Bodies, Ph. D. Thesis, University of Maryland.

  • R.C. Browne (1977) Dynamic Stability of Viscoelastic Rods, Workshop on Existence Theory in Non-Linear Elasticity, University of Texas at Austin.

    Google Scholar 

  • C.M. Dafermos (1969) The mixed initial-boundary problem for the equations of non-linear viscoelasticity, J. of Differential Equations 6, 71–81.

    Google Scholar 

  • J. Dieudonné (1960) Foundations of Modern Analysis, Academic Press, New York.

    Google Scholar 

  • J.M. Greenberg (1969) On the existence, uniqueness, and stability of the equation 282-01, J. of Anal. Appl. 25, 575–591.

    Google Scholar 

  • J.M. Greenberg, R.C. Macamy & V.J. Mizel (1968) On the existence, uniqueness, and stability of the equation 282-02, J. of Math. Mech., 17, 707–728.

    Google Scholar 

  • A. Friedman (1969) Partial Differential Equations, Holt. Rinehart, Winston, New York-Chicago.

    Google Scholar 

  • R.J. Knops (1977) Workshop on Existence Theory in Non-Linear Elasticity, University of Texas at Austin.

    Google Scholar 

  • R.J. Knops & E.W. Wilkes (1973) Theory of Elastic Stability. Handbuch der Physik Vol. VIa/3, Springer-Verlag, Berlin-Heidelberg-New York.

    Google Scholar 

  • O.A. Ladyženskaya & Solonnikov (1967) Boundary Value Problems of Mathematical Physics III, Proceedings of the Steklov Institute of Mathematics 83. English translation: American Mathematical Society, Providence, Rhode Island.

    Google Scholar 

  • A. Pazy (1974) Semigroups of Linear Operators and Applications to Partial Differential Equations, University of Maryland, Department of Mathematics Lecture Notes #10.

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  1. Mathematics Research Center, University of Wisconsin, Madison

    Russell C. Browne

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  1. Russell C. Browne
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Communicated by S. Antman

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Browne, R.C. Dynamic stability of one-dimensional nonlinearly viscoelastic bodies. Arch. Rational Mech. Anal. 68, 257–282 (1978). https://doi.org/10.1007/BF00247742

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