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Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 29))

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Abstract

The purpose of this paper is to discuss the asymptotic behavior as t ➔ +∞ of solutions to semilinear equations of the form

$$ {{\phi }_{t}} = A\phi + J(\phi ) $$
(1.1)

where φ(t) takes values in a Banach space B, and A generates a Co semigroup on B. Of particular interest is the stability of equilibrium or periodic solutions of (1.1).

This research partially supported by the National Science Foundations under grant NSF GP 34260

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References

  1. H. Brezis, Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, in Contributions to Nonlinear Functional Analysis, E. Zarontonello ed., Academic Press, New York, 1971.

    Google Scholar 

  2. H. Brezis, Quelque proprieties des operateurs monotones et des semigroup nonlinear, Proc. of Nato Conference Brussels 1975, to appear.

    Google Scholar 

  3. C. Dafermos and M. Slemrod, Asymptotic behavior of nonlinear contraction semigroups, Jnl. Funct. Anal., 13 (1973), 97–106.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Diedonné, Foundations of Modern Analysis, Academic Press, New York, 1960.

    Google Scholar 

  5. E. Hille and R. Phillips, Functional Analysis and Semigroups, Am. Math. Soc. Collquium Publ Vol. 31, 1957.

    MATH  Google Scholar 

  6. P.D. Lax and R.S. Phillips, Scattering Theory, Academic Press, New York, 1967.

    MATH  Google Scholar 

  7. W. Littman, The wave operator and Lp norms, J. Math. Mech. 12 (1963), 55–68.

    MathSciNet  MATH  Google Scholar 

  8. P.J.McKenna and J. Rauch, Strongly nonlinear elliptic boundary value problems with kernel, to appear.

    Google Scholar 

  9. J.Rauch, Qualitative behavior of dissipative wave equations on bounded domains, Archiv. Rat. Mech. Anal., 1976.

    Google Scholar 

  10. J.Rauch, Global existence for the FitzHugh-Nagumo Equations, Comm. P.D.E., (to appear)

    Google Scholar 

  11. J. Rauch and J. Smoller, Strongly nonlinear perturbations of nonnegative boundary value problems with kernel, to appear.

    Google Scholar 

  12. M.Reed, Abstract Non-Linear Wave Equations, Springer Lecture Notes no 507, Springer-Verlag, New York, 1976.

    Google Scholar 

  13. D.Sattinger, Stability of nonlinear hyperbolic equations, Archi. Rat. Mech. Anal., 28 (1968) 226–244.

    MathSciNet  MATH  Google Scholar 

  14. W. Strauss, Nonlinear scattering theory, Proceedings Nato Advanced Study Institute June 1973, D. Reidel Publishing Co., Holland.

    Google Scholar 

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© 1977 D. Reidel Publishing Company, Dordrecht-Holland

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Rauch, J. (1977). Stability of Motion for Semilinear Equations. In: Garnir, H.G. (eds) Boundary Value Problems for Linear Evolution Partial Differential Equations. NATO Advanced Study Institutes Series, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1205-8_7

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  • DOI: https://doi.org/10.1007/978-94-010-1205-8_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-1207-2

  • Online ISBN: 978-94-010-1205-8

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