On solutions to the initial-boundary value problem for ∂/∂tu-Δβ(u)=ƒ

Mitsuhiro NAKAO

doi:10.2969/jmsj/03510071

Mitsuhiro NAKAO

著者情報

ジャーナルフリー

1983 年 35 巻 1 号 p. 71-83

DOI https://doi.org/10.2969/jmsj/03510071

詳細

Published: 1983 Received: 1980/12/15 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: 論文タイトル訂正内容: Wrong : On solutions to the initial-boundary value problem for ∂/∂tu-Δβ(u)=f
Right : On solutions to the initial-boundary value problem for ∂/∂tu-Δβ(u)=ƒ

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) D. G. Aronson, Regularity properties of flows through porous media, SIAM J. Appl. Math., 17 (1969), 461-467.
2) F. V. Atkinson and L. A. Peletier, Similarity solutions of the nonlinear diffusion equations, Arch. Rational Mech. Anal., 54 (1974) , 373-392.
3) J. E. Boillet, D. A. D. Saravia and L. T. Villa, Similarity solutions of the equation of one-dimensional heat conduction, J. Differential Equations, 35 (1980), 55-65.
4) H. Brezis, On some degenerate nonlinear parabolic equations; Nonlinear functional analysis, Proc. Symp. Pure Math. A. M. S., 18 (1970) , 28-38.
5) H. Brezis, Monotonicity method in Hilbert spaces and some applications to nonlinear partial differential equations, Contributions to nonlinear functional analysis, Academic Press, New York-London, 1971, 101-156.
6) M. G. Crandall, Semigroups of nonlinear transformations in Banach spaces, Contributions to nonlinear functional analysis, Academic Press, New York-London, 1971, 157-179.
7) J. A. Dubinskii, Weak convergence in nonlinear elliptic and parabolic equations, Amer. Math. Soc. Transl., (2) 67 (1968), 226-258.
8) S. L. Kamenomostskaya, On stefan's problem, Mat. Sb., 53 (1961) , 489-514.
9) Y. Konishi, Une méthode de résolution d'une équation d'évolution nonlinéaire dégénérée, J. Fac. Sci. Univ. Tokyo Sect. IA, 19 (1972) , 243-255.
10) Y. Konishi, On the nonlinear semi-groups associated with u_t=Δβ(u) and φ(u_t)=Δu, J. Math. Soc. Japan, 25 (1973), 622-628.
11) O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tseva, Linear and quasilinear equations of parabolic type, Amer. Math. Soc., Providence, R. I., 1968.
12) J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non-inéaires, Dunod, Paris, 1969.
13) M. Nakao, Convergence of solutions of the wave equation with a nonlinear dissipative term to the steady state, Mem. Fac. Sci. Kyushu Univ. Ser. A, 30 (1976), 257-265.
14) M. Nakao, Decay of solutions of some nonlinear evolution equations, J. Math. Anal. Appl., 60 (1977), 542-549.
15) M. Nakao, A difference inequality and its application to nonlinear evolution equations, J. Math. Soc. Japan, 30 (1978), 747-762.
16) O. A. Oleinik, A. S. Kalashnikov and Chzhou Yui-Lin, The Cauchy problem and boundary problems for equations of the type of nonstationary filtration, Izv. Akad. Nauk SSSR, Ser. Mat., 22 (1958), 667-704.
17) L. A. Peletier, Asymptotic behaviour of temperature profiles of a class of non-linear heat conduction problems, Quart. J. Mech. Appl. Math., 23 (1970), 441-447.
18) P. A. Raviart, Sur la résolution et l'approximation de certaines équations paraboliques non linéaires dégénérées, Arch. Rat. Mech. Anal., 25 (1967), 64-80.

Right : [1] D. G. Aronson, Regularity properties of flows through porous media, SIAM J. Appl. Math., 17 (1969), 461-467.
[2] F. V. Atkinson and L. A. Peletier, Similarity solutions of the nonlinear diffusion equations, Arch. Rational Mech. Anal., 54 (1974) , 373-392.
[3] J. E. Boillet, D. A. D. Saravia and L. T. Villa, Similarity solutions of the equation of one-dimensional heat conduction, J. Differential Equations, 35 (1980), 55-65.
[4] H. Brezis, On some degenerate nonlinear parabolic equations; Nonlinear functional analysis, Proc. Symp. Pure Math. A. M. S., 18 (1970), 28-38.
[5] H. Brezis, Monotonicity method in Hilbert spaces and some applications to nonlinear partial differential equations, Contributions to nonlinear functional analysis, Academic Press, New York-London, 1971, 101-156.
[6] M. G. Crandall, Semigroups of nonlinear transformations in Banach spaces, Contributions to nonlinear functional analysis, Academic Press, New York-London, 1971, 157-179.
[7] J. A. Dubinskii, Weak convergence in nonlinear elliptic and parabolic equations, Amer. Math. Soc. Transl., (2) 67 (1968), 226-258.
[8] S. L. Kamenomostskaya, On stefan's problem, Mat. Sb., 53 (1961) , 489-514.
[9] Y. Konishi, Une méthode de résolution d'une équation d'évolution nonlinéaire dégénérée, J. Fac. Sci. Univ. Tokyo Sect. IA, 19 (1972), 243-255.
[10] Y. Konishi, On the nonlinear semi-groups associated with u_t=Δβ(u) and φ(u_t)=Δu, J. Math. Soc. Japan, 25 (1973), 622-628.
[11] O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tseva, Linear and quasilinear equations of parabolic type, Amer. Math. Soc., Providence, R. I., 1968.
[12] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non-inéaires, Dunod, Paris, 1969.
[13] M. Nakao, Convergence of solutions of the wave equation with a nonlinear dissipative term to the steady state, Mem. Fac. Sci. Kyushu Univ. Ser. A, 30 (1976), 257-265.
[14] M. Nakao, Decay of solutions of some nonlinear evolution equations, J. Math. Anal. Appl., 60 (1977), 542-549.
[15] M. Nakao, A difference inequality and its application to nonlinear evolution equations, J. Math. Soc. Japan, 30 (1978), 747-762.
[16] O. A. Oleinik, A. S. Kalashnikov and Chzhou Yui-Lin, The Cauchy problem and boundary problems for equations of the type of nonstationary filtration, Izv. Akad. Nauk SSSR, Ser. Mat., 22 (1958), 667-704.
[17] L. A. Peletier, Asymptotic behaviour of temperature profiles of a class of non-linear heat conduction problems, Quart. J. Mech. Appl. Math., 23 (1970), 441-447.
[18] P. A. Raviart, Sur la résolution et l'approximation de certaines équations paraboliques non linéaires dégénérées, Arch. Rat. Mech. Anal., 25 (1967), 64-80.

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）