Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

EVOLUTION EQUATIONS ASSOCIATED WITH TIME{DEPENDENT SUBDIFFERENTIALS

  • Received : 2009.05.19
  • Published : 2011.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we study the solvability of parabolic equations governed by the difference of time dependent subdifferential and time independent subdifferential in reflexive Banach spaces.

Keywords

References

  1. R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
  2. G. Akagi, Doubly nonlinear evolution equations governed by time-dependent subdiffer-entials in reflexive Banach spaces, J. Differential Equations 231 (2006), no. 1, 32-56. https://doi.org/10.1016/j.jde.2006.04.006
  3. G. Akagi and M. Otani, Evolution inclusions governed by the difference of two sub-differentials in reflexive Banach spaces, J. Differential Equations 209 (2005), no. 2, 392-415. https://doi.org/10.1016/j.jde.2004.08.011
  4. G. Akagi and M. Otani, Time-dependent constraint problems arising from macroscopic critical-state models for type-II superconductivity and their approximations, Adv. Math. Sci. Appl. 14 (2004), no. 2, 683-712.
  5. V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noord-hoff Intl. Publ., Leyden, 1976.
  6. H. Brezis, Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, Math. Studies, Vol. 5, North-Holland, Amsterdam/New York, 1973.
  7. H. Ishii, Asymptotic stability and blowing up of solutions of some nonlinear equations, J. Differential Equations 26 (1977), no. 2, 291-319. https://doi.org/10.1016/0022-0396(77)90196-6
  8. N. Kenmochi, Some nonlinear parabolic variational inequalities, Israel J. Math. 22 (1975), no. 3-4, 304-331. https://doi.org/10.1007/BF02761596
  9. Y. Koi and J. Watanabe, On nonlinear evolution equations with a difference term of subdifferentials, Proc. Japan Acad. 52 (1976), no. 8, 413-416. https://doi.org/10.3792/pja/1195518240
  10. J. L. Lions, Quelques methodes de resolution des problemes aux limites non lineaires, Dunod; Gauthier-Villars, Paris 1969.
  11. M. Otani, Nonmonotone perturbations for nonlinear parabolic equations associated with subdifferential operators, J. Differential Equations 46 (1982), no. 2, 268-299. https://doi.org/10.1016/0022-0396(82)90119-X