Periodic stability of solutions to some degenerate parabolic equations with dynamic boundary conditions

Toyohiko AIKI

doi:10.2969/jmsj/04810037

Toyohiko AIKI

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1996 Volume 48 Issue 1 Pages 37-59

DOI https://doi.org/10.2969/jmsj/04810037

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Published: 1996 Received: September 10, 1993 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) T. Aiki, Multi-dimensional Stefan problems with dynamic boundary conditions, Tech. Rep. Math. Sci., Chiba Univ., No. 18, 1992.
2) T. Aiki, N. Kenmochi and J. Shinoda, Periodic stability for some degenerate parabolic equations with nonlinear flux conditions, Nonlinear Anal. TMA., 17 (1991), 885-902.
3) H. Attouch and A. Damlamian, Problèmes d'évolution Bans les Hilbert et applications, J. Math. Pures Appl., 54 (1975), 53-74.
4) H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions daps les spaces de Hilbert, North-Holland, Amsterdam, 1973.
5) A. Damlamian, Some results on the multi-phase Stefan problem, Comm. Partial Differential Equations, 2 (1977), 1017-1044.
6) A. Damlamian and N. Kenmochi, Periodicity and almost periodicity of solutions to a multi-phase Stefan problem in several space variables, Nonlinear Anal. TMA., 12 (1988), 921-934.
7) A. Haraux and N. Kenmochi, Asymptotic behavior of solutions to some degenerate parabolic equations, Funkcial Ekvac., 34 (1991), 19-38.
8) N. Kenmochi, Solvability of nonlinear evolution equations with time-dependent constraints and applications, Bull. Fac. Education, Chiba Univ., 30 (1981), 1-87.
9) N. Kenmochi and M. Ôtani, Asymptotic behavior of periodic systems generated by time-dependent subdifferential operators, Funkcial. Ekvac., 29 (1986), 219-236.
10) N. Kenmochi and M. Ôtani, Nonlinear evolution equations governed by subdifferential operators with almost periodic time-dependence, Rend. Accad. Naz. Sci. XL Mem. Mat., 104 (1986), 288-291.
11) R. E. Langer, A problem in diffusion or in the flow of heat for a solid in contact with fluid, Tôhoku Math. J., Ser. 1, 35 (1932), 260-275.
12) A. Mikelic and M. Primicerio, Homogenization of the heat equation for a domain with a network of pipes with a well-mixed fluid, to appear.
13) M. Niezgodka and I. Pawlow, A generalized Stefan problem in several space variables, Appl. Math. Optim., 9 (1983), 193-224.
14) M. Niezgodka, I. Pawlow and A. Visintin, Remarks on the paper by A. Visintin, Sur le problème de Stefan avec flux non linéaire, Boll. Un. Mat. Ital., Anal. Funz. Appl. Serie V, 18 (1981), 87-88.
15) M. Primicerio and J. F. Rodrigues, The Hele-Shaw problem with nonlocal injection condition, Nonlinear Mathematical Problems in Industry, Gakuto, Tokyo, 1993.
16) A. Visintin, Sur le problème de Stefan avec flux non linéaire, Boll. Un. Mat. Ital., Anal. Funz. Appl. Serie V, 18 (1981), 63-86.

Right : [1] T. Aiki, Multi-dimensional Stefan problems with dynamic boundary conditions, Tech. Rep. Math. Sci., Chiba Univ., No. 18, 1992.
[2] T. Aiki, N. Kenmochi and J. Shinoda, Periodic stability for some degenerate parabolic equations with nonlinear flux conditions, Nonlinear Anal. TMA., 17 (1991), 885-902.
[3] H. Attouch and A. Damlamian, Problèmes d'évolution dans les Hilbert et applications, J. Math. Pures Appl., 54 (1975), 53-74.
[4] H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les spaces de Hilbert, North-Holland, Amsterdam, 1973.
[5] A. Damlamian, Some results on the multi-phase Stefan problem, Comm. Partial Differential Equations, 2 (1977), 1017-1044.
[6] A. Damlamian and N. Kenmochi, Periodicity and almost periodicity of solutions to a multi-phase Stefan problem in several space variables, Nonlinear Anal. TMA., 12 (1988), 921-934.
[7] A. Haraux and N. Kenmochi, Asymptotic behavior of solutions to some degenerate parabolic equations, Funkcial Ekvac., 34 (1991), 19-38.
[8] N. Kenmochi, Solvability of nonlinear evolution equations with time-dependent constraints and applications, Bull. Fac. Education, Chiba Univ., 30 (1981), 1-87.
[9] N. Kenmochi and M. Ôtani, Asymptotic behavior of periodic systems generated by time-dependent subdifferential operators, Funkcial. Ekvac., 29 (1986), 219-236.
[10] N. Kenmochi and M. Ôtani, Nonlinear evolution equations governed by subdifferential operators with almost periodic time-dependence, Rend. Accad. Naz. Sci. XL Mem. Mat., 104 (1986), 288-291.
[11] R. E. Langer, A problem in diffusion or in the flow of heat for a solid in contact with fluid, Tôhoku Math. J., Ser. 1, 35 (1932), 260-275.
[12] A. Mikelic and M. Primicerio, Homogenization of the heat equation for a domain with a network of pipes with a well-mixed fluid, to appear.
[13] M. Niezgodka and I. Pawlow, A generalized Stefan problem in several space variables, Appl. Math. Optim., 9 (1983), 193-224.
[14] M. Niezgodka, I. Pawlow and A. Visintin, Remarks on the paper by A. Visintin, Sur le problème de Stefan avec flux non linéaire, Boll. Un. Mat. Ital., Anal. Funz. Appl. Serie V, 18 (1981), 87-88.
[15] M. Primicerio and J. F. Rodrigues, The Hele-Shaw problem with nonlocal injection condition, Nonlinear Mathematical Problems in Industry, Gakuto, Tokyo, 1993.
[16] A. Visintin, Sur le problème de Stefan avec flux non linéaire, Boll. Un. Mat. Ital., Anal. Funz. Appl. Serie V, 18 (1981), 63-86.

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