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Boundary approximate controllability of some linear parabolic systems
Solvability of $p$-Laplacian parabolic logistic equations with constraints coupled with Navier-Stokes equations in 2D domains
1. | Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan |
References:
[1] |
V. Barbu, Nonlinear Differential Equations of Monotone Types in Banach Spaces, Springer, New York, 2010.
doi: 10.1007/978-1-4419-5542-5. |
[2] |
J. L. Boldrini and S. A. Lorca, The initial value problem for a generalized Boussinesq model, Nonlinear Anal., 36 (1999), 457-480.
doi: 10.1016/S0362-546X(97)00635-4. |
[3] |
J. I. Díaz and G. Galiano, Existence and uniqueness of solutions of the Boussinesq system with nonlinear thermal diffusion, Topol. Methods Nonlinear Anal., 11 (1998), 59-82. |
[4] |
T. Fukao and N. Kenmochi, Stefan problems with convection governed by Navier-Stokes equations, Adv. Math. Sci. Appl., 15 (2005), 29-48. |
[5] |
T. Fukao and M. Kubo, Nonlinear degenerate parabolic equations for a thermohydraulic model, in Discrete Contin. Dyn. Syst., Am. Inst. Math. Sci., (2007), 399-408. |
[6] |
T. Fukao and M. Kubo, Time-dependent double obstacle problem in thermohydraulics, in Nonlinear phenomena with energy dissipation, GAKUTO Internat. Ser. Math. Sci. Appl., Gakkōtosho, Tokyo, 29 (2008), 73-92. |
[7] |
M. Kubo, Weak solutions of a thermohydraulics model with a general nonlinear heat flux, in Mathematical approach to nonlinear phenomena: Modelling, analysis and simulations, GAKUTO Internat. Ser. Math. Sci. Appl., Gakkōtosho, Tokyo, 23 (2005), 163-178. |
[8] |
H. Morimoto, Nonstationary Boussinesq equations, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 39 (1992), 61-75. |
[9] |
N. Okazawa, An application of the perturbation theorem for $m$-accretive operators, II, Proc. Japan Acad. Ser. A Math. Sci., 60 (1984), 1-42.
doi: 10.3792/pjaa.60.10. |
[10] |
J. Simon, Compact sets in the space $L^p(0,T;B)$, Ann. Mat. Pura Appl., 146 (1987), 65-96.
doi: 10.1007/BF01762360. |
[11] |
M. Sobajima, Y. Tsuzuki and T. Yokota, Existence and uniqueness of solutions to nonlinear heat equations with constraints coupled with Navier-Stokes equations in 2D domains, Adv. Math. Sci. Appl., 22 (2012), 577-596. |
[12] |
R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, Amsterdam-New York, North-Holland, 1977. |
show all references
References:
[1] |
V. Barbu, Nonlinear Differential Equations of Monotone Types in Banach Spaces, Springer, New York, 2010.
doi: 10.1007/978-1-4419-5542-5. |
[2] |
J. L. Boldrini and S. A. Lorca, The initial value problem for a generalized Boussinesq model, Nonlinear Anal., 36 (1999), 457-480.
doi: 10.1016/S0362-546X(97)00635-4. |
[3] |
J. I. Díaz and G. Galiano, Existence and uniqueness of solutions of the Boussinesq system with nonlinear thermal diffusion, Topol. Methods Nonlinear Anal., 11 (1998), 59-82. |
[4] |
T. Fukao and N. Kenmochi, Stefan problems with convection governed by Navier-Stokes equations, Adv. Math. Sci. Appl., 15 (2005), 29-48. |
[5] |
T. Fukao and M. Kubo, Nonlinear degenerate parabolic equations for a thermohydraulic model, in Discrete Contin. Dyn. Syst., Am. Inst. Math. Sci., (2007), 399-408. |
[6] |
T. Fukao and M. Kubo, Time-dependent double obstacle problem in thermohydraulics, in Nonlinear phenomena with energy dissipation, GAKUTO Internat. Ser. Math. Sci. Appl., Gakkōtosho, Tokyo, 29 (2008), 73-92. |
[7] |
M. Kubo, Weak solutions of a thermohydraulics model with a general nonlinear heat flux, in Mathematical approach to nonlinear phenomena: Modelling, analysis and simulations, GAKUTO Internat. Ser. Math. Sci. Appl., Gakkōtosho, Tokyo, 23 (2005), 163-178. |
[8] |
H. Morimoto, Nonstationary Boussinesq equations, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 39 (1992), 61-75. |
[9] |
N. Okazawa, An application of the perturbation theorem for $m$-accretive operators, II, Proc. Japan Acad. Ser. A Math. Sci., 60 (1984), 1-42.
doi: 10.3792/pjaa.60.10. |
[10] |
J. Simon, Compact sets in the space $L^p(0,T;B)$, Ann. Mat. Pura Appl., 146 (1987), 65-96.
doi: 10.1007/BF01762360. |
[11] |
M. Sobajima, Y. Tsuzuki and T. Yokota, Existence and uniqueness of solutions to nonlinear heat equations with constraints coupled with Navier-Stokes equations in 2D domains, Adv. Math. Sci. Appl., 22 (2012), 577-596. |
[12] |
R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, Amsterdam-New York, North-Holland, 1977. |
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