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Abstract

A nonlinear parabolic Volterra integrodifferential equation with infinite delay, of relevance in population theory, is considered. Under a suitable spectral condition, approximation results are given for solutions near to equilibria in an appropriate function space.

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References

  1. Chen, G., Grimmer, R.: Well-posedness and Approximations of linear Volterra Integrodifferential Equations in Banach Spaces, in Volterra Equations, Londen, S.-O. and Staffans, O. J., Eds., Berlin-Heidelberg-New York, Springer 1979.

    Google Scholar 

  2. Cushing, J. M.: Integrodifferential Equations and Delay Models in Population Dynamics, Berlin-Heidelberg-New York, Springer 1977.

    Book  Google Scholar 

  3. Hille, E., Phillips, R. S.: Functional Analysis and Semigroups, Amer. Math. Soc. Coll. Publ., Providence, AMS, 1957.

    Google Scholar 

  4. Iannelli, M.: On the Green Function for Abstract Evolution Equation, Boll. U.M.I. 6 (1972), 154–174.

    Google Scholar 

  5. Kato, T.: Linear Evolution Equations of “Hyperbolic” Type, II., J. Math. Soc. Japan 25 (1973), 648–666.

    Article  Google Scholar 

  6. Miller, R. K.: Asymptotic Stability and Perturbations for Linear Volterra Integrodifferential Systems, in Delay and Functional Differential Equations and Their Applications, Schmitt, K., Ed., New York-London, Academic Press, 1972.

    Google Scholar 

  7. Miller, R. K.: Volterra Integral Equations in a Banach Space, Funkc. Ekv. 18 (1975), 163–194.

    Google Scholar 

  8. Schiaffino, A., Tesei, A.: On the Asymptotic Stability for Abstract Volterra Integro-differential Equations, Rend. Acc. Naz. Lincei 67 (1979) (in press).

    Google Scholar 

  9. Schiaffino, A., Tesei, A.: Asymptotic Stability Properties for Nonlinear Diffusion Volterra Equations, Rend. Acc. Naz. Lincei, 67 (1979) (in press).

    Google Scholar 

  10. Tesei, A.: Stability Properties for Partial Volterra Integro-differential Equations, Ann. Mat. Pura Appl. (to appear).

    Google Scholar 

  11. Trigiante, D.: Asymptotic Stability and Discretization on an Infinite Interval, Computing 18 (1977), 117–129.

    Article  Google Scholar 

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© 1980 Springer Basel AG

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Tesei, A. (1980). Approximation Results for Volterra Integro-Partial Differential Equations. In: Albrecht, J., Collatz, L. (eds) Numerical Treatment of Integral Equations / Numerische Behandlung von Integralgleichungen. International Series of Numerical Mathematics / International Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 53. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6314-8_16

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  • DOI: https://doi.org/10.1007/978-3-0348-6314-8_16

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-1105-6

  • Online ISBN: 978-3-0348-6314-8

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