On the nonlinear semi-groups associated with ut=Δβ(u) and φ(ut)=Δu

Yoshio KONISHI

doi:10.2969/jmsj/02540622

On the nonlinear semi-groups associated with u_t=Δβ(u) and φ(u_t)=Δu

Yoshio KONISHI

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ジャーナルフリー

1973 年 25 巻 4 号 p. 622-628

DOI https://doi.org/10.2969/jmsj/02540622

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Published: 1973 Received: 1972/11/13 Available on J-STAGE: 2006/09/29 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/09/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) H. Brezis and W. A. Strauss, Semi-linear second-order elliptic equations in L¹, J. Math. Soc. Japan (to appear).
2) M. G. Crandall, Semigroups of nonlinear transformations in Banach spaces.Contributions to Nonlinear Functional Analysis, Academic Press, New York-London, 1971, 157-179.
3) M. G. Crandall, A generalized domain for semigroup generators, MRC Technical Summary Report #1189, Madison, Wisconsin (to appear in Proc. Amer. Math. Soc.).
4) M. G. Crandall and T. M. Liggett, Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math., 93 (1971), 265-298.
5) Y. Komura, Result of Crandall-Liggett and some open problems. Semi-groups and evolution equations, Kokyuroku, RIMS Kyoto Univ., 134 (1972), 1-5 (in Japanese).
6) Y. Konishi, Some examples of nonlinear semi-groups in Banach lattices, J. Fac. Sci. Univ. Tokyo Sect. IA, 18 (1972), 537-543.
7) Y. Konishi, On the uniform convergence of a finite difference scheme for a nonlinear heat equation, Proc. Japan Acad., 48 (1972), 62-66.
8) Y. Konishi, On u_t=u_xx-F(u_x) and the differentiability of the nonlinear semigroup associated with it, Proc. Japan Acad., 48 (1972), 281-286.
9) Y. Konishi, Une méthode de résolution d'une équation d'évolution non linéairedégénérée, J. Fac. Sci. Univ. Tokyo Sect. IA, 19 (1972), 243-255.
10) Y. Konishi, Sur un système dégénéré des équations paraboliques semi-linéairesavec les conditions aux limites non linéaires, J. Fac. Sci. Univ. Tokyo Sect. IA, 19 (1972), 353-361.
11) K. Masuda, On the integration of diffusion equations in some function spaces, I (to appear).
12) S. Oharu, A note on the generation of nonlinear semigroups in a locally convex space, Proc. Japan Acad., 43 (1967), 847-851.
13) K. Sato, On the generators of non-negative contraction semi-groups in Banach lattices, J. Math. Soc. Japan, 20 (1968), 423-436.
14) W. A. Strauss, Evolution equations non-linear in the time derivative, J. Math. Mech., 15 (1966), 49-82.
15) W. A. Strauss, The Energy Method in Nonlinear Partial Differential Equations, Lecture Notes (1967), IMPA, Notas de Matemática, Rio de Janeiro.
16) K. Yosida, Functional Analysis, Springer, Berlin-Heidelberg-New York (1971).

Right : [1] H. Brezis and W. A. Strauss, Semi-linear second-order elliptic equations in L¹, J. Math. Soc. Japan (to appear).
[2] M. G. Crandall, Semigroups of nonlinear transformations in Banach spaces.Contributions to Nonlinear Functional Analysis, Academic Press, New York-London, 1971, 157-179.
[3] M. G. Crandall, A generalized domain for semigroup generators, MRC Technical Summary Report #1189, Madison, Wisconsin (to appear in Proc. Amer. Math. Soc.).
[4] M. G. Crandall and T. M. Liggett, Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math., 93 (1971), 265-298.
[5] Y. Komura, Result of Crandall-Liggett and some open problems. Semi-groups and evolution equations, Kokyuroku, RIMS Kyoto Univ., 134 (1972), 1-5 (in Japanese).
[6] Y. Konishi, Some examples of nonlinear semi-groups in Banach lattices, J. Fac. Sci. Univ. Tokyo Sect. IA, 18 (1972), 537-543.
[7] Y. Konishi, On the uniform convergence of a finite difference scheme for a nonlinear heat equation, Proc. Japan Acad., 48 (1972), 62-66.
[8] Y. Konishi, On u_t=u_xx-F(u_x) and the differentiability of the nonlinear semigroup associated with it, Proc. Japan Acad., 48 (1972), 281-286.
[9] Y. Konishi, Une méthode de résolution d'une équation d'évolution non linéairedégénérée, J. Fac. Sci. Univ. Tokyo Sect. IA, 19 (1972), 243-255.
[10] Y. Konishi, Sur un système dégénéré des équations paraboliques semi-linéairesavec les conditions aux limites non linéaires, J. Fac. Sci. Univ. Tokyo Sect. IA, 19 (1972), 353-361.
[11] K. Masuda, On the integration of diffusion equations in some function spaces, I (to appear).
[12] S. Ôharu, A note on the generation of nonlinear semigroups in a locally convex space, Proc. Japan Acad., 43 (1967), 847-851.
[13] K. Sato, On the generators of non-negative contraction semi-groups in Banach lattices, J. Math. Soc. Japan, 20 (1968), 423-436.
[14] W. A. Strauss, Evolution equations non-linear in the time derivative, J. Math. Mech., 15 (1966), 49-82.
[15] W. A. Strauss, The Energy Method in Nonlinear Partial Differential Equations, Lecture Notes (1967), IMPA, Notas de Matemática, Rio de Janeiro.
[16] K. Yosida, Functional Analysis, Springer, Berlin-Heidelberg-New York (1971).

訂正日: 2006/09/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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