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Asymptotic behaviour for a class of delayed cooperative models with patch structure
Singular limit of viscous Cahn-Hilliard equations with memory and dynamic boundary conditions
1. | Department of Mathematics, Florida International University, Miami, FL, 33199, United States |
2. | Dipartimento di Matematica, Politecnico di Milano, 20133 Milano |
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doi: 10.3934/dcds.2010.28.275. |
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in "Handbook of Differential Equations: Evolutionary Equations," Vol. IV, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, (2008), 201-228.
doi: 10.1016/S1874-5717(08)00004-2. |
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Commun. Pure Appl. Anal., 5 (2006), 609-614. |
[56] |
Adv. Math. Sci. Appl., 11 (2001), 505-529. |
[57] |
Ann. Mat. Pura Appl. (4), 185 (2006), 627-648.
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Comm. Comp. Phys., 1 (2006), 1-52. Google Scholar |
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in "Nonlinear Partial Differential Equations and their Applications," GAKUTO Internat. Ser. Math. Sci. Appl., 20, Gakkotōsho, Tokyo, (2004), 266-276. |
[60] |
Adv. Differential Equations, 8 (2003), 83-110. |
[61] |
Comm. Partial Differential Equations, 24 (1999), 1055-1077.
doi: 10.1080/03605309908821458. |
[62] |
Math. Models Methods Appl. Sci., 17 (2007), 411-437.
doi: 10.1142/S0218202507001978. |
[63] |
Second edition, Applied Mathematical Sciences, 68, Springer-Verlag, New York, 1997. |
[64] |
J. Math. Anal. Appl., 328 (2007), 789-812.
doi: 10.1016/j.jmaa.2006.05.075. |
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J. Differential Equations, 204 (2004), 511-531.
doi: 10.1016/j.jde.2004.05.004. |
show all references
References:
[1] |
NoDEA Nonlinear Differential Equations Appl., 17 (2010), 663-695.
doi: 10.1007/s00030-010-0075-0. |
[2] |
J. Chem. Phys., 28 (1958), 258-267. Google Scholar |
[3] |
Nonlinear Anal., 72 (2010), 2375-2399.
doi: 10.1016/j.na.2009.11.002. |
[4] |
Asymptot. Anal., 71 (2011), 123-162. |
[5] |
American Mathematical Society Colloquium Publications, 49, American Mathematical Society, Providence, RI, 2002. |
[6] |
Math. Nachr., 13 (2006), 1448-1462.
doi: 10.1002/mana.200410431. |
[7] |
Nonlinear Anal., 72 (2010), 1668-1682.
doi: 10.1016/j.na.2009.09.006. |
[8] |
Quart. Appl. Math., 68 (2010), 607-643. |
[9] |
Math. Meth. Appl. Sci., 32 (2009), 1370-1395.
doi: 10.1002/mma.1091. |
[10] |
Indiana Univ. Math. J., 55 (2006), 169-215.
doi: 10.1512/iumj.2006.55.2661. |
[11] |
Arch. Rational Mech. Anal., 37 (1970), 297-308. |
[12] |
Ann. Rev. Fluid Mech., 11 (1979), 371-400. Google Scholar |
[13] |
Math. Nachr., 272 (2004), 11-31.
doi: 10.1002/mana.200310186. |
[14] |
Phys. Rev. Letters, 79 (1997), 893-896. Google Scholar |
[15] |
Europhys. Letters, 42 (1998), 49-54. Google Scholar |
[16] |
Math. Methods Appl. Sci., 29 (2006), 2009-2036.
doi: 10.1002/mma.757. |
[17] |
Dyn. Partial Differ. Equ., 5 (2008), 39-67. |
[18] |
Commun. Pure Appl. Anal., 7 (2008), 819-836.
doi: 10.3934/cpaa.2008.7.819. |
[19] |
C. G. Gal, Exponential attractors for a Cahn-Hilliard model in bounded domains with permeable walls,, Electron. J. Differential Equations, 2006 ().
|
[20] |
C. G. Gal, G. R. Goldstein, J. A. Goldstein, S. Romanelli and M. Warma, Fredholm alternative, semilinear elliptic problems, and Wentzell boundary conditions,, submitted., (). Google Scholar |
[21] |
Nonlinear Anal. Real World Appl., 10 (2009), 1738-1766.
doi: 10.1016/j.nonrwa.2008.02.013. |
[22] |
Discrete Contin. Dyn. Syst. Ser. S, 2 (2009), 113-147.
doi: 10.3934/dcdss.2009.2.113. |
[23] |
Discrete Contin. Dyn. Syst., 22 (2008), 1041-1063.
doi: 10.3934/dcds.2008.22.1041. |
[24] |
Phys. Rev. E, 71 (2005), 046125, 13 pp. Google Scholar |
[25] |
Phys. A, 388 (2009), 3113-3123.
doi: 10.1016/j.physa.2009.04.003. |
[26] |
Philos. Mag. Lett., 87 (2007), 821-827. Google Scholar |
[27] |
Int. J. Thermodyn., 11 (2008), 21-28. Google Scholar |
[28] |
Phys. Lett. A, 372 (2008), 985-989. Google Scholar |
[29] |
Math. Models Methods Appl. Sci., 15 (2005), 165-198.
doi: 10.1142/S0218202505000327. |
[30] |
Nonlinearity, 18 (2005), 1859-1883.
doi: 10.1088/0951-7715/18/4/023. |
[31] |
in "Dissipative Phase Transitions," Ser. Adv. Math. Appl. Sci., 71, World Sci. Publ., Hackensack, NJ, (2006), 101-114.
doi: 10.1142/9789812774293_0006. |
[32] |
Proc. Royal Soc. Edinburgh Sect. A, 140 (2010), 329-366.
doi: 10.1017/S0308210509000365. |
[33] |
Rend. Cl. Sci. Mat. Nat., 141 (2007), 129-161. |
[34] |
Comm. Pure Appl. Anal., 8 (2009), 881-912.
doi: 10.3934/cpaa.2009.8.881. |
[35] |
Phys. D, 240 (2011), 754-766.
doi: 10.1016/j.physd.2010.12.007. |
[36] |
Asymptot. Anal., 56 (2008), 229-249. |
[37] |
Asymptot. Anal., 33 (2003), 261-320. |
[38] |
J. Evol. Equ., 9 (2009), 371-404.
doi: 10.1007/s00028-009-0017-7. |
[39] |
Comm. Partial Differential Equations, 34 (2009), 137-170.
doi: 10.1080/03605300802608247. |
[40] |
Nonlinearity, 23 (2010), 707-737.
doi: 10.1088/0951-7715/23/3/016. |
[41] |
in "Evolution Equations, Semigroups and Functional Analysis" (eds. A. Lorenzi and B. Ruf) (Milano, 2000), Progr. Nonlinear Differential Equations Appl., 50, Birkhäuser, Basel, (2002), 155-178. |
[42] |
J. Differential Equations, 239 (2007), 38-60.
doi: 10.1016/j.jde.2007.05.003. |
[43] |
Phys. D, 92 (1996), 178-192.
doi: 10.1016/0167-2789(95)00173-5. |
[44] |
Colloq. Math., 109 (2007), 217-229.
doi: 10.4064/cm109-2-4. |
[45] |
Topol. Methods Nonlinear Anal., 32 (2008), 327-345. |
[46] |
Reprint of the 1980 edition, Classics in Mathematics, Springer-Verlag, Berlin, 1995. |
[47] |
Computer Phys. Comm., 133 (2001), 139-157.
doi: 10.1016/S0010-4655(00)00159-4. |
[48] |
Eur. Phys. J. Special Topics, 177 (2009), 165-175. Google Scholar |
[49] |
J. Evol. Equ., 7 (2007), 59-78.
doi: 10.1007/s00028-006-0235-1. |
[50] |
Math. Models Appl. Sci., 28 (2005), 709-735.
doi: 10.1002/mma.590. |
[51] |
in "Handbook of Differential Equations: Evolutionary Equations," Vol. IV, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, (2008), 103-200.
doi: 10.1016/S1874-5717(08)00003-0. |
[52] |
Discrete Contin. Dyn. Syst., 28 (2010), 275-310.
doi: 10.3934/dcds.2010.28.275. |
[53] |
in "Material Instabilities in Continuum Mechanics" (Edinburgh, 1985-1986), Oxford Sci. Publ., Oxford Univ. Press, New York, (1988), 329-342. |
[54] |
in "Handbook of Differential Equations: Evolutionary Equations," Vol. IV, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, (2008), 201-228.
doi: 10.1016/S1874-5717(08)00004-2. |
[55] |
Commun. Pure Appl. Anal., 5 (2006), 609-614. |
[56] |
Adv. Math. Sci. Appl., 11 (2001), 505-529. |
[57] |
Ann. Mat. Pura Appl. (4), 185 (2006), 627-648.
doi: 10.1007/s10231-005-0175-3. |
[58] |
Comm. Comp. Phys., 1 (2006), 1-52. Google Scholar |
[59] |
in "Nonlinear Partial Differential Equations and their Applications," GAKUTO Internat. Ser. Math. Sci. Appl., 20, Gakkotōsho, Tokyo, (2004), 266-276. |
[60] |
Adv. Differential Equations, 8 (2003), 83-110. |
[61] |
Comm. Partial Differential Equations, 24 (1999), 1055-1077.
doi: 10.1080/03605309908821458. |
[62] |
Math. Models Methods Appl. Sci., 17 (2007), 411-437.
doi: 10.1142/S0218202507001978. |
[63] |
Second edition, Applied Mathematical Sciences, 68, Springer-Verlag, New York, 1997. |
[64] |
J. Math. Anal. Appl., 328 (2007), 789-812.
doi: 10.1016/j.jmaa.2006.05.075. |
[65] |
J. Differential Equations, 204 (2004), 511-531.
doi: 10.1016/j.jde.2004.05.004. |
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