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A nonlinear hyperbolic volterra equation

Part of the Lecture Notes in Mathematics book series (LNM,volume 737)

Abstract

A mathematical model for the motion of a nonlinear one dimensional viscoelastic rod is analysed by an energy method developed by C.M. Dafermos and the author. Global existence, uniqueness, boundedness, and the decay of smooth solutions as t → ∞ are established for sufficiently smooth and "small" data.

Keywords

  • Volterra Equation
  • Global Smooth Solution
  • Resolvent Kernel
  • Quasilinear Wave Equation
  • Banach Fixed Point Theorem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

sponsored by the United States Army under Grant No. DAAG 29-77-G-0004 and under Contract No. DAAG 29-75-C-0024.

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References

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© 1979 Springer-Verlag

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Nohel, J.A. (1979). A nonlinear hyperbolic volterra equation. In: Londen, SO., Staffans, O.J. (eds) Volterra Equations. Lecture Notes in Mathematics, vol 737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064509

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  • DOI: https://doi.org/10.1007/BFb0064509

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09534-7

  • Online ISBN: 978-3-540-35035-4

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