Pacific Journal of Mathematics

Nonlinear holomorphic semigroups.

T. L. Hayden and F. J. Massey, III

Article information

Source
Pacific J. Math., Volume 57, Number 2 (1975), 423-439.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102905997

Mathematical Reviews number (MathSciNet)
MR0390855

Zentralblatt MATH identifier
0304.47059

Subjects
Primary: 47H15
Secondary: 35K15: Initial value problems for second-order parabolic equations

Citation

Hayden, T. L.; Massey, F. J. Nonlinear holomorphic semigroups. Pacific J. Math. 57 (1975), no. 2, 423--439. https://projecteuclid.org/euclid.pjm/1102905997


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References

  • [1] S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partialdifferentialequations satisfyinggeneral boundary conditions, I, Comm. Pure Appl. Math., 12 (1959), 623-727.
  • [2] H. Brezis, Proprietes regularisantes de certains semi-groups non lineaires, Israel J. Math., 9 (1971), 513-534.
  • [3] H. Brzis, M. G. Crandall and A. Pazy, Perturbations of nonlinear maximal monotone sets in Banach space, Comm. Pure Appl. Math., 23 (1970), 123-144.
  • [4] H. Brezis and W. Strauss, Semi-linear second-order elliptic equations in L, J. Math. Soc. Japan, to appear.
  • [5] M. Crandall and T. Liggett, Generation of semi-groups of nonlineartransformations on general Banach spaces, Amer. J. Math., 93 (1971), 265-298.
  • [6] M. Crandall and A. Pazy, Semi-groups of nonlinearcontractions and dissipative sets, J. Functional Analysis, 3 (1969), 376-418.
  • [7] G. Da Prato, Somme d'applications non lineaires, Symposia Mathematica VII, 1st. Naz. di Alta Mat., Academic Press, London, 1971.
  • [8] A. Friedman, PartialDifferentialEquations,Holt, Rinehart and Winston, New York, 1969.
  • [9] H. Fujita and T. Kato, On the Navier-Stokesinitialvalue problem, I, Arch. Rational Mech. Anal., 16 (1964), 269-315.
  • [10] D. Henry, Geometric theory of semilinear parabolic equations, mimeographed notes, University of Kentucky, 1974.
  • [11] E. Hille and R. S. Phillips, Functionalanalysisand semi-groups, revised, ed., Amer. Math. Soc. Colloq. Publ., Vol. 31, Amer. Math. Soc, Providence, 1957.
  • [12] T. Kato, Perturbationtheory for linear operators, Die Grundlehren der math. Wissenschaften, Band 132, Springer-Verlag, New York, 1966.
  • [13] T. Kato,Nonlinearsemigroups and evolution equations, J. Math. Soc. Japan, 19 (1967), 508-520.
  • [14] T. Kato, Accretive operators and nonlinear evolution equations in Banach spaces, Proc. Symp. Pure Math. 18, Part I, Amer. Math. Soc, Providence, 138-161 (1968).
  • [15] Y. Kmura, Nonlinear semi-groups in Hilbert space, J. Math. Soc. Japan, 19 (1967), 493-507.
  • [16] Y. Kmura, Differentiabilityof nonlinear semigroups, J. Math. Soc. Japan, 21 (1969), 375-402.
  • [17] Y. Konishi, Some examples of nonlinear semi-groups in Banach lattices, J. Fac. Sci. Univ. Tokyo, 18 (1972), 537-543.
  • [18] S. G. Krein, Linear differentialequations in a Banach space, Translations of Mathematical Monographs, Vol. 29, Amer. Math. Soc, Providence, 1971.
  • [19] K. Masuda, On the analyticity and the unique continuation theorem for solutions of the Navier-Stokes equation, Proc. Japan Acad., 43 (1967), 827-832.
  • [20] I. Miyadera, Some remarks on semigroups of nonlinear operators, Thoku Math. J., 23 (1971), 245-258.
  • [21] J. W. Neuberger, Existence of a spectrum for nonlinear transformations,Pacific J. Math., 31 (1969), 157-159.
  • [22] S. Ouchi, On the analyticity in time of solutions of initial boundary value problems for semilinear parabolic differential equations with monotone nonlinearity,J. Fac. Sci. Univ. Tokyo, 2O (1974), 19-41.
  • [23] P. E. Sobolevskii, Equations of parabolic type in a Banach space, TrudyMoscow Mat. Obsc. 10(1961), 297-350; English transl., Amer. Math. Soc. Transl. (2) 49(1965), 1-62.
  • [24] K. Yosida, Functional analysis, 2nd ed., Die Grundlehren der math. Wissenschaften, Band 123, Springer-Verlag, New York, 1968.