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Existence and multiplicity of stationary solutions for a Cahn--Hilliard-type equation in $\mathbb{R}^N$
1. | Universidad Carlos III de Madrid, Av. Universidad 30, 28911-Leganés, Spain |
References:
[1] |
P. Álvarez-Caudevilla, J.D. Evans and V.A. Galaktionov, Countable families of solutions of a limit stationary semilinear fourth-order Cahn-Hilliard-type equation I., Mountain Pass Theorem and Lusternik-Schnirel'man patterns in $\mathbbR^N$, ().
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[2] |
P. Álvarez-Caudevilla and V.A. Galaktionov, Steady states, global existence and blow-up for fourth-order semilinear parabolic equations of Cahn-Hilliard type, Advances Nonl. Stud., 12 (2012), 315-361. |
[3] |
A. Ambrosetti and P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), 349-381. |
[4] |
J.D. Evans, V.A. Galaktionov and J.F. Williams, Blow-up and global asymptotics of the limit unstable Cahn-Hilliard equation, SIAM J. Math. Anal., 38 (2006), 64-102. |
[5] |
V.A. Galaktionov, E. Mitidieri and S.I. Pohozaev, Variational approach to complicated similarity solutions of higher-order nonlinear PDEs. II, Nonl. Anal.: RWA, 12 (2011), 2435-2466 (arXiv:1103.2643). |
[6] |
G.A. Klassen and E. Mitidieri, Standing wave solutions for a system derived from the FitzHugh-Nagumo equations for nerve conduction, SIAM J. Math. Anal., 17 (1986), 74-83. |
[7] |
A. Novick-Cohen, The Cahn-Hilliard equation: mathematical and modeling perspectives, Adv. Math. Sci. Appl., 8 (1998), 965-985. |
[8] |
L.A. Peletier and W.C. Troy, Spatial Patterns. Higher Order Models in Physics and Mechanics, Birkhäusser, Boston/Berlin, 2001. |
show all references
References:
[1] |
P. Álvarez-Caudevilla, J.D. Evans and V.A. Galaktionov, Countable families of solutions of a limit stationary semilinear fourth-order Cahn-Hilliard-type equation I., Mountain Pass Theorem and Lusternik-Schnirel'man patterns in $\mathbbR^N$, ().
|
[2] |
P. Álvarez-Caudevilla and V.A. Galaktionov, Steady states, global existence and blow-up for fourth-order semilinear parabolic equations of Cahn-Hilliard type, Advances Nonl. Stud., 12 (2012), 315-361. |
[3] |
A. Ambrosetti and P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), 349-381. |
[4] |
J.D. Evans, V.A. Galaktionov and J.F. Williams, Blow-up and global asymptotics of the limit unstable Cahn-Hilliard equation, SIAM J. Math. Anal., 38 (2006), 64-102. |
[5] |
V.A. Galaktionov, E. Mitidieri and S.I. Pohozaev, Variational approach to complicated similarity solutions of higher-order nonlinear PDEs. II, Nonl. Anal.: RWA, 12 (2011), 2435-2466 (arXiv:1103.2643). |
[6] |
G.A. Klassen and E. Mitidieri, Standing wave solutions for a system derived from the FitzHugh-Nagumo equations for nerve conduction, SIAM J. Math. Anal., 17 (1986), 74-83. |
[7] |
A. Novick-Cohen, The Cahn-Hilliard equation: mathematical and modeling perspectives, Adv. Math. Sci. Appl., 8 (1998), 965-985. |
[8] |
L.A. Peletier and W.C. Troy, Spatial Patterns. Higher Order Models in Physics and Mechanics, Birkhäusser, Boston/Berlin, 2001. |
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