Nonlinear perturbations and abstract evolution equations in general banach spaces

  • Gabriella Di Blasio


Part I deals with the problem of determining sufficient conditions under which the sum of two m-accretive operators on a closed convex set Q1 is m-accretive on Q1. Part II is concerned with the initial value problem: u′+Au+g(u)=v, u(0)=u0. Applications are given to the Boltzmann equation.


Evolution Equation Boltzmann Equation Nonlinear Perturbation Abstract Evolution Abstract Evolution Equation 
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.


  1. [1]
    V. Barbu,Continuous perturbations of non-linear m-accretive operators in Banach spaces, Boll. U.M.I.,6 (1972), pp. 270–278.zbMATHMathSciNetGoogle Scholar
  2. [2]
    R. Bodmer,Zur Boltzmanngleichung, Zürich, Seminar für Theor. Phys. E.T.H.Google Scholar
  3. [3]
    H. Brézis,Opérateurs maximaux monotones et semi-groupes de contraction dans les espaces de Hilbert, Math. Studies 5, North-Holland (1973).Google Scholar
  4. [4]
    F. E. Browder,Nonlinear accretive operators in Banach spaces, Bull. Am. Soc.,73 (1967), pp. 470–476.zbMATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    C. Cercignani,Mathematical methods in kinetic theory, N. Y., Plenum Press (1969).zbMATHGoogle Scholar
  6. [6]
    G. da Prato,Somme d'applications non-linéarires, Symposia Mathematica, VII (1971), pp. 233–268.Google Scholar
  7. [7]
    G. Da Prato:Applications croissantes et équations d'évolutions dans les espaces de Banach, to appear.Google Scholar
  8. [8]
    G. Da Prato - P. Grisvard,Somme d'opérateurs linéaires et équations differentielles opérationnelles, J. Math. pures et appl., to appear.Google Scholar
  9. [9]
    G. Di Blasio,Strong solutions for Boltzmann equation in the spatially homogeneous case, Boll. U.M.I.,8 (1973), pp. 127–136.zbMATHGoogle Scholar
  10. [10]
    G. Di Blasio,Differentiability of spatially homogeneous solutions of the Boltzmann equation in the non Maxwellian case, Comm. Math. Phys.,38 (1974), pp. 331–340.CrossRefzbMATHMathSciNetGoogle Scholar
  11. [11]
    G. Di Blasio,Somme d'opérateurs non linéaires et application à l'équation de Boltzmann, C. R. Acad. Sc.,280, série A (1975), pp. 1121–1123.zbMATHGoogle Scholar
  12. [12]
    H. Grad,Principles of kinetic theory of gases, Handbuch der Physik,12, Berlin - Göttingen - Heidelberg, Springer (1958).Google Scholar
  13. [13]
    M. Iannelli,A note on some non-linear non contraction semigroup, Boll. U.M.I.,6 (1970), pp. 1015–1025.MathSciNetGoogle Scholar
  14. [14]
    T. Kato,Nonlinear semigroups and evolution equations, J. Math. Soc. Japan,19 (1967), pp. 508–520.zbMATHMathSciNetCrossRefGoogle Scholar
  15. [15]
    T. Kato,Accretive operators and nonlinear evolution equations in Banach spaces, Proc. Symp. Pure Math.,18, Part I, A.M.S. Providence, R. I. (1968), pp. 138–161.Google Scholar
  16. [16]
    J. L. Lions,Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod-Gauthier Villars (1969).Google Scholar
  17. [17]
    R. H. Martin Jr.,Differential equations on closed subsets of a Banach space, Trans. Amer. Math. Soc.,179 (1973), pp. 399–414.CrossRefzbMATHMathSciNetGoogle Scholar
  18. [18]
    R. H. Martin Jr.,Invariant sets for perturbed semigroups of linear operators, to appear.Google Scholar
  19. [19]
    G. Webb,Nonlinear perturbations of linear accretive operators in Banach spaces, Journal of Funct. An.,10 (1972), pp. 191–203.CrossRefzbMATHMathSciNetGoogle Scholar
  20. [20]
    A. Ja. Povzner,The Boltzmann equation in the kinetic theory of gases, Mat. Sbornik,58 (1962), pp. 65–86; translated in A.M.S. Translation, Series 2,47 (1965), pp. 193–216.zbMATHMathSciNetGoogle Scholar

Copyright information

© Fondazione Annali di Matematica Para ed Applicata 1975

Authors and Affiliations

  • Gabriella Di Blasio
    • 1
  1. 1.Roma

Personalised recommendations