Difference approximation of Cauchy problems for quasi-dissipative operators and generation of nonlinear semigroups

Yoshikazu KOBAYASHI

doi:10.2969/jmsj/02740640

Yoshikazu KOBAYASHI

著者情報

ジャーナルフリー

1975 年 27 巻 4 号 p. 640-665

DOI https://doi.org/10.2969/jmsj/02740640

詳細

Published: 1975 Received: 1975/04/08 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 所属機関情報訂正内容: 訂正前 :
1) Department of Mathematics Faculty of Engineering Niigata University
2) Department of Mathematics Faculty of Engineering Niigata University

訂正後 :
1) Department of Mathematics School of Science and Engineering Waseda University
2) Department of Mathematics Faculty of Engineering Niigata University

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) V. Barbu, Continuous perturbations of nonlinear m-accretive operators in Banach spaces, Boll. Un. Mat. Ital., 6 (1972), 270-278.
2) Ph. Bénilan, Equations d'évolution dans un espace de Banach quelconque et applications, These Orsay, 1972.
3) Ph. Bénilan, Equations d'évolution dans un espace de Banach quelconque, Ann. Inst. Fourier, to appear.
4) H. Brezis, Operateurs maximaux monotones et semigroups de contractions dans les espaces de Hilbert, North Holland Publ. Co., Amesterdam, 1973.
5) H. Brezis and A. Pazy, Accretive sets and differential equations in Banach spaces, Israel J. Math., 8 (1970), 367-383.
6) M. Crandall and C. Evans, On the relation of the operator ∂/∂s+∂/∂τ to evolution governed by accretive operator, to appear.
7) M. Crandall and T. Liggett, Generation of semigroups of nonlinear transfor-mations in general Banach spaces, Amer. J. Math., 93 (1970), 265-298.
8) T. Kato, Accretive operators and nonlinear evolution equations in Banach spaces, Proc. Symp. Pure Math., 18 (1970), 138-161.
9) N. Kenmochi and S. Oharu, Difference approximation of nonlinear evolution equations, Publ. Res. Inst. Math. Sci., 10 (1974), 147-207.
10) Y. Kobayashi, Difference approximation of evolution equations and generation of nonlinear semigroups, Proc. Japan Acad., 51 (1975), 406-410.
11) Y. Kobayashi and K. Kobayasi, Criteria for m-dissipativity of nonlinear operators in general Banach spaces, to appear.
12) R. Martin, Differential equations on closed subsets of a Banach space, Trans. Amer. Math. Soc., 179 (1973), 399-414.
13) R. Martin, Approximation and existence of solutions to ordinary differential equations in Banach spaces, Funkcial. Ekvac., 16 (1973), 195-211.
14) M. Pierre, Perturbations localment Lipschitziennes et continues d'operateurs m-accretifs, to appear.
15) S. Rasmussen, Nonlinear semigroups, evolution equations and product integral representations, Various Publications Series, No. 2, Aarhaus Universitet. 1971/72.
16) T. Takahashi, Difference approximation of Cauchy problems for quasi-dissipative operators and generation of semigroups of nonlinear contractions, to appear.
17) T. Takahashi, Convergence of difference approximation of nonlinear evolution equations and generation of semigroups, to appear.
18) T. Takahashi, Invariant sets for semigroups of nonlinear operators, to appear.
19) G. Webb, Continuous nonlinear perturbations of linear accretive operators in Banach spaces, J. Funct. Anal., 10 (1972), 191-203.
20) J. Yorke, Ordinary differential equations and evolutionary equations, preprint.
21) K. Yosida, Functional Analysis, Fourth edition, Springer Verlag, 1974.

Right : [1] V. Barbu, Continuous perturbations of nonlinear m-accretive operators in Banach spaces, Boll. Un. Mat. Ital., 6 (1972), 270-278.
[2] Ph. Bénilan, Equations d'évolution dans un espace de Banach quelconque et applications, These Orsay, 1972.
[3] Ph. Bénilan, Equations d'évolution dans un espace de Banach quelconque, Ann. Inst. Fourier, to appear.
[4] H. Brezis, Operateurs maximaux monotones et semigroups de contractions dans les espaces de Hilbert, North Holland Publ. Co., Amesterdam, 1973.
[5] H. Brezis and A. Pazy, Accretive sets and differential equations in Banach spaces, Israel J. Math., 8 (1970), 367-383.
[6] M. Crandall and C. Evans, On the relation of the operator ∂/∂s+∂/∂τ to evolution governed by accretive operator, to appear.
[7] M. Crandall and T. Liggett, Generation of semigroups of nonlinear transformations in general Banach spaces, Amer. J. Math., 93 (1970), 265-298.
[8] T. Kato, Accretive operators and nonlinear evolution equations in Banach spaces, Proc. Symp. Pure Math., 18 (1970), 138-161.
[9] N. Kenmochi and S. Oharu, Difference approximation of nonlinear evolution equations, Publ. Res. Inst. Math. Sci., 10 (1974), 147-207.
[10] Y. Kobayashi, Difference approximation of evolution equations and generation of nonlinear semigroups, Proc. Japan Acad., 51 (1975), 406-410.
[11] Y. Kobayashi and K. Kobayasi, Criteria for m-dissipativity of nonlinear operators in general Banach spaces, to appear.
[12] R. Martin, Differential equations on closed subsets of a Banach space, Trans. Amer. Math. Soc., 179 (1973), 399-414.
[13] R. Martin, Approximation and existence of solutions to ordinary differential equations in Banach spaces, Funkcial. Ekvac., 16 (1973), 195-211.
[14] M. Pierre, Perturbations localment Lipschitziennes et continues d'operateurs m-accretifs, to appear.
[15] S. Rasmussen, Nonlinear semigroups, evolution equations and product integral representations, Various Publications Series, No. 2, Aarhaus Universitet. 1971/72.
[16] T. Takahashi, Difference approximation of Cauchy problems for quasi-dissipative operators and generation of semigroups of nonlinear contractions, to appear.
[17] T. Takahashi, Convergence of difference approximation of nonlinear evolution equations and generation of semigroups, to appear.
[18] T. Takahashi, Invariant sets for semigroups of nonlinear operators, to appear.
[19] G. Webb, Continuous nonlinear perturbations of linear accretive operators in Banach spaces, J. Funct. Anal., 10 (1972), 191-203.
[20] J. Yorke, Ordinary differential equations and evolutionary equations, preprint.
[21] K. Yosida, Functional Analysis, Fourth edition, Springer Verlag, 1974.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

責任著者(Corresponding author)

訂正情報

J-STAGEへの登録はこちら（無料）