Hiroshima Mathematical Journal

Weak solutions for certain nonlinear time-dependent parabolic variational inequalities

Nobuyuki Kenmochi and Toshitaka Nagai

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 5, Number 3 (1975), 525-535.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206136544

Digital Object Identifier
doi:10.32917/hmj/1206136544

Mathematical Reviews number (MathSciNet)
MR0394346

Zentralblatt MATH identifier
0348.35051

Subjects
Primary: 47H15
Secondary: 35R20: Partial operator-differential equations (i.e., PDE on finite- dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx]

Citation

Kenmochi, Nobuyuki; Nagai, Toshitaka. Weak solutions for certain nonlinear time-dependent parabolic variational inequalities. Hiroshima Math. J. 5 (1975), no. 3, 525--535. doi:10.32917/hmj/1206136544. https://projecteuclid.org/euclid.hmj/1206136544


Export citation

References

  • [1] H.Attouch, Ph. Benilan, A. Damlamian and C. Picard, Equations devolution avec condition unilateral^ C.R. Acad. Sci.Paris Ser.A-B279 (1974), A607-A609.
  • [2] H.Attouch and A. Damlamian, Problernes d'evolution dans lesHubert et applications, preprint.
  • [3] H. Brezis, Perturbations non lineaires d'operateurs maximaux monotones, C. R.Acad. Sci. Paris Ser. A-B 269 (1969), A566-A569.
  • [4] H. Brezis, Un probleme devolution avec contraintes unilaterales dependant du temps, C. R. Acad. Paris Ser. A-B 274 (1972), A310-A312.
  • [5] H. Brezis, Problemes unilateraux, J. Math. Pures Appl. 51 (1972), 1-168.
  • [6] F. E. Browder, Problemes non lineaires, Montreal Univ. Press, Montreal, 1966.
  • [7] G. Duvaut, Resolution d'un probleme de Stefan (Fusion d'un bloc de glace a zero degre), C. R. Acad. Sci. Paris Ser. A-B 276 (1973), A1461-A1463.
  • [8] N. Kenmochi, The semi-discretisation method and nonlinear time-dependent parabolic variational inequalities, Proc. Japan Acad. 50 (1974), 714-717.
  • [9] N. Kenmochi, Pseudomonotone operators and nonlinear elliptic boundary value problems, J. Math. Soc. Japan 27 (1975), 121-149.
  • [10] N. Kenmochi, Some nonlinear parabolic variational inequalities, Israel J. Math, (to appear).
  • [11] N. Kenmochi, Initial-boundary value problems for nonlinear parabolic partial differential equations (manuscript).
  • [12] J. L. Lions, Quelques methodes de resolution de problemes aux limites non lineaires, Dunod Gauthier-Villars, Paris, 1969.
  • [13] W. Littman, G. Stampacchia and H. F. Weinberger, Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa 17 (1963), 45--79.
  • [14-] J J Moreau, Probleme devolution associe a un convexe mobile d'un espace hilbertien, C. R. Acad. Sci. Paris Ser. A-B 276 (1973), A791-A794.
  • [15] J. C. Peralba, Un probleme devolution relatif a un operateur sous-differentiel dependant du temps, C. R. Acad. Sci. Paris Ser. A-B 275 (1972), A93-A96.
  • [16] R. T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc. 149 (1970), 75-88.
  • [17] J. Watanabe, On certain nonlinear evolution equations, J. Math. Soc. Japan 25 (1973), 446-463.