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Semigroups of locally lipschitzian operators and applications

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1540)

Keywords

  • Strong Solution
  • Mild Solution
  • Differential Inclusion
  • Nonlinear Evolution Equation
  • Range Condition

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References

  1. Ph. Bénilan, Equations d'évolution dans un espace de Banach quelconque et applications, Thèsis, Orsay, 1972.

    Google Scholar 

  2. J. Chambers and S. Oharu, Semi-groups of local Lipschitzians in a Banach space, Pacific J. Math., 39(1971), pp. 89–112.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. M. Crandall and T. Liggett, Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math., 93(1971), 265–298.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. M. Crandall and L. Evans, On the relation of operator ∂/∂s+∂/∂τ to evolution governed by accretive operators, Israel J. math., 21(1975), 261–278.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. M. Crandall, Nonlinear semigroups and evolution governed by accretive operators, Proc. Symp. in Pure Math., 43, Part 2, Amer. Math. Soc., Providence, R. I., 1986.

    MATH  Google Scholar 

  6. T. Kato, Accretive operators and nonlinear evolution equations in Banach spaces, in Nonlinear Functional Analysis, Proc. Symp. in Pure Math., 18, Amer. Math. Soc., Providence, R. I., 1970, 138–161.

    CrossRef  Google Scholar 

  7. N. Kenmochi and S. Oharu, Difference approximation of nonlinear evolution equations and semigroups of nonlinear operators, Publ. R. I. M. S., Kyoto Univ., 10(1974), 147–207.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Y. Kōmura, Nonlinear semigroups in Hilbert spaces, J. Math. Soc. Japan, 19(1967), 503–520.

    MATH  Google Scholar 

  9. Y. Kobayashi, Difference approximation of Cauchy of problems for quasi-dissipative operators and generation of nonlinear semigroups, J. Math. Soc. Japan, 27(1975), 640–665.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Y. Kobayashi and S. Oharu, Semigroups of locally Lipschitzian operators in Banach spaces, Hiroshima Math. J., 20(1990), 573–611.

    MathSciNet  MATH  Google Scholar 

  11. K. Kobayasi, Y. Kobayashi and S. Oharu, Nonlinear evolution operators in Banach spaces, Osaka J. Math., 21(1984), 281–310.

    MathSciNet  MATH  Google Scholar 

  12. V. Lakshmikantham and S. Leela, Nonlinear Differential Equations in Abstract Spaces, International Series in Nonlinear Mathematics, 2, Pergamon Press, 1981.

    Google Scholar 

  13. J. L. Lions, Quelques Méthodes de Résolution des Problème aux Limites Nonlinéairs, Paris Dunod, Gauthiers-Villars, 1969.

    MATH  Google Scholar 

  14. J. L. Lions and G. Prodi, Un théorème d'existence et d'unicité dans les équations de Navier-Stokes en dimension 2, C. R. Acad. Sci., Paris, 248(1959), 3519–3521.

    MathSciNet  MATH  Google Scholar 

  15. S. Oharu and T. Takahashi, Locally Lipschitz continuous perturbations of linear dissipative operators and nonlinear semigroups, Proc. Amer. Math. Soc., 100(1987), 187–194.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. A. Pazy, Semigroups of nonlinear contractions and their asymptotic behavior, in Nonlinear Analysis and Mechanics, edited by R. J. Knops, Heriot-Watt Sympos., Vol. 3, Pitman Research Notes in math., 30, 1979, 36–134.

    Google Scholar 

  17. M. Pierre, Génération et perturbation de semi-groupes de contractions nonlinéaires, Thèse de Docteur de 3 é cycle, Université de Paris VI, 1976.

    Google Scholar 

  18. M. Pierre, Un théoreme général de generation de semigroupes Nonlinéaires, Israel J. Math., 23(1976), 189–199.

    CrossRef  MathSciNet  Google Scholar 

  19. M. Schechter, Interpolation of nonlinear partial differential operators and generation of differential evolutions, J. Diff. Eq., 46(1982), 78–102.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, 1983.

    Google Scholar 

  21. T. Takahashi, Convergence of difference approximations of nonlinear evolution equations and generation of semigroups, J. Math. Soc. Japan, 28(1976), 96–113.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis, North-Holand, 1979.

    Google Scholar 

  23. Z. Yoshida and Y. Giga, A nonlinear semigroup approach to the Navier Stokes system, Comm. in Partial Differential Equations, 9(1984), 215–230.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. K. Yosida, Functional Analysis, 6th edition, Springer-Verlag, 1980.

    Google Scholar 

  25. J. Walker, Dynamical Systems and Evolutions, Theory and Applications, Prenum Press, 1980.

    Google Scholar 

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© 1993 Springer-Verlag

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Kobayashi, Y., Oharu, S. (1993). Semigroups of locally lipschitzian operators and applications. In: Komatsu, H. (eds) Functional Analysis and Related Topics, 1991. Lecture Notes in Mathematics, vol 1540. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085480

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  • DOI: https://doi.org/10.1007/BFb0085480

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56471-3

  • Online ISBN: 978-3-540-47565-1

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