Abstract and Applied Analysis

Quasi-Hyperbolicity and Delay Semigroups

Shard Rastogi and Sachi Srivastava

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We study quasi-hyperbolicity of the delay semigroup associated with the equation u(t)=Bu(t)+Φut, where ut is the history function and (B,D(B)) is the generator of a quasi-hyperbolic semigroup. We give conditions under which the associated solution semigroup of this equation generates a quasi-hyperbolic semigroup.

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Abstr. Appl. Anal., Volume 2016 (2016), Article ID 1984874, 6 pages.

Received: 1 June 2016
Accepted: 28 September 2016
First available in Project Euclid: 17 December 2016

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Rastogi, Shard; Srivastava, Sachi. Quasi-Hyperbolicity and Delay Semigroups. Abstr. Appl. Anal. 2016 (2016), Article ID 1984874, 6 pages. doi:10.1155/2016/1984874. https://projecteuclid.org/euclid.aaa/1481943741

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  • J. K. Hale, Functional Differential Equation, vol. 3 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1971.
  • G. F. Webb, “Functional differential equations and nonlinear semigroups in \emphL$^{P}$-spaces,” Journal of Differential Equations, vol. 20, no. 1, pp. 71–89, 1976.
  • A. Bátkai, “Hyperbolicity of linear partial differential equations with delay,” Integral Equations and Operator Theory, vol. 44, no. 4, pp. 383–396, 2002.
  • A. Batkai, E. Fasanga, and R. Shvidkoy, “Hyperbolicity of delay equations via Fourier multipliers,” Acta Scientiarum Mathematicarum, vol. 69, no. 1-2, pp. 131–145, 2003.
  • C. J. K. Batty and Y. Tomilov, “Quasi-hyperbolic semigroups,” Journal of Functional Analysis, vol. 258, no. 11, pp. 3855–3878, 2010.
  • C. J. Batty, “Differentiability and growth bounds of solutions of delay equations,” Journal of Mathematical Analysis and Applications, vol. 299, no. 1, pp. 133–146, 2004.
  • Y. Latushkin and R. Shvidkoy, “Hyperbolicity of semigroups and fourier multipliers,” in Systems, Approximation, Singular Integral Operators, and Related Topics (Bordeaux, 2000), vol. 129 of Operator Theory: Advances and Applications, pp. 341–363, Birkhäuser, Basel, Switzerland, 2000. \endinput