-
1
-
-
0000988067
-
Stability of singularly perturbed solutions to systems of reaction- diffusion equations
-
Y. Nishiura and H. Fujii, Stability of singularly perturbed solutions to systems of reaction- diffusion equations, SIAM J. Math. Anal., 18 (1987), 1726-1770.
-
(1987)
SIAM J. Math. Anal.
, vol.18
, pp. 1726-1770
-
-
Nishiura, Y.1
Fujii, H.2
-
2
-
-
0000130504
-
Layer oscillations in reaction-diffusion systems
-
Y. Nishiura and M. Mimura, Layer oscillations in reaction-diffusion systems, SIAM J.Appl. Math., 49 (1989), 481-514.
-
(1989)
SIAM J.Appl. Math.
, vol.49
, pp. 481-514
-
-
Nishiura, Y.1
Mimura, M.2
-
3
-
-
0000518462
-
Scenarios of domain pattern formation in a reaction-diffusion system
-
C. B. Muratov and V. Osipov, Scenarios of domain pattern formation in a reaction-diffusion system, Phys. Rev. E., 54 (1996), 4860-4879. (Pubitemid 126589748)
-
(1996)
Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
, vol.54
, Issue.5
, pp. 4860-4879
-
-
Muratov, C.B.1
Osipov, V.V.2
-
4
-
-
0000334408
-
Fast reaction slow diffusion and curve shortening
-
J. Rubinstein, P. Sternberg and J. B. Keller, Fast reaction, slow diffusion, and curve shortening, SIAM J. Appl. Math., 49 (1989), 116-133.
-
(1989)
SIAM J. Appl. Math.
, vol.49
, pp. 116-133
-
-
Rubinstein, J.1
Sternberg, P.2
Keller, J.B.3
-
5
-
-
0000518461
-
Interface proliferation and the growth of labyrinths in a reaction-diffusion system
-
R. E. Goldstein, D. J. Muraki and D. M. Petrich, Interface proliferation and the growth of labyrinths in a reaction-diffusion system, Phys. Rev. E., 53 (1996), 3933-3957. (Pubitemid 126558900)
-
(1996)
Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
, vol.53
, Issue.4 SUPPL. B
, pp. 3933-3957
-
-
Goldstein, R.E.1
Muraki, D.J.2
Petrich, D.M.3
-
6
-
-
83455180735
-
Self-organization in non-equilibrium systems
-
New York
-
G. Nicolis and I. Prigogine, "Self-organization in Non-Equilibrium Systems," Wiley Inter-science, New York, 1977.
-
(1977)
Wiley Inter-Science
-
-
Nicolis, G.1
Prigogine, I.2
-
10
-
-
83455241732
-
Dissipative localized structures in extended systems
-
M. Taki, M. Tlidi and T. Kolokolnikov, eds., "Dissipative Localized Structures in Extended Systems," Chaos Focus issue, 17, 2007.
-
(2007)
Chaos Focus Issue
, vol.17
-
-
Taki, M.1
Tlidi, M.2
Kolokolnikov, T.3
-
11
-
-
35648966560
-
Self-replication of mesa patterns in reaction-diffusion systems
-
DOI 10.1016/j.physd.2007.07.014, PII S0167278907002564
-
T. Kolokolnikov, M. Ward and J. Wei, Self-replication of mesa patterns in reaction-diffusion models, Physica D, 236 (2007), 104-122. (Pubitemid 350026086)
-
(2007)
Physica D: Nonlinear Phenomena
, vol.236
, Issue.2
, pp. 104-122
-
-
Kolokolnikov, T.1
Ward, M.J.2
Wei, J.3
-
12
-
-
23044528996
-
Monotonicity of stable solutions in shadow systems
-
W.-M. Ni, P. Poláčik and E. Yanagida, Monotonicity of stable solutions in shadow systems, Trans. A.M.S., 352 (2001), 5057-5069. (Pubitemid 33766436)
-
(2001)
Transactions of the American Mathematical Society
, vol.353
, Issue.12
, pp. 5057-5069
-
-
Ni, W.-M.1
Polacik, P.2
Yanagida, E.3
-
13
-
-
0000518460
-
General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems
-
(MR1388221) C. Muratov and V. V. Osipov, General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems, Phys, Rev. E., 53 (1996), 3101-3116. (Pubitemid 126583994)
-
(1996)
Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
, vol.53
, Issue.4
, pp. 3101-3116
-
-
Muratov, C.B.1
Osipov, V.V.2
-
14
-
-
33746216397
-
A reaction-diffusion memory device
-
DOI 10.1002/anie.200600400
-
A. Kaminaga, V. K. Vanag and I. R. Epstein, A reaction-diffusion memory device, Ange- wandte chemie, 45 (2006), 3087-3089. (Pubitemid 44099023)
-
(2006)
Angewandte Chemie - International Edition
, vol.45
, Issue.19
, pp. 3087-3089
-
-
Kaminaga, A.1
Vanag, V.K.2
Epstein, I.R.3
-
15
-
-
18744415463
-
Black spots in a surfactant-rich Belousov- Zhabotinsky reaction dispersed in a water-in-oil microemulsion system
-
A. Kaminaga, V. K. Vanag and I. R. Epstein, Black spots in a surfactant-rich Belousov- Zhabotinsky reaction dispersed in a water-in-oil microemulsion system, J. Chem. Phys., 122 (2005), 061747.
-
(2005)
J. Chem. Phys.
, vol.122
, pp. 061747
-
-
Kaminaga, A.1
Vanag, V.K.2
Epstein, I.R.3
-
16
-
-
34247859041
-
Spot deformation and replication in the two-dimensional Belousov-Zhabotinski reaction in a water-in-oil microemulsion system
-
T. Kolokolnikov and M. Tlidi, Spot deformation and replication in the two-dimensional Belousov-Zhabotinski reaction in a water-in-oil microemulsion system, Phys. Rev. Lett., 98 (2007), 188-303.
-
(2007)
Phys. Rev. Lett.
, vol.98
, pp. 188-303
-
-
Kolokolnikov, T.1
Tlidi, M.2
-
17
-
-
31144461544
-
Mesa-type patterns in the one-dimensional Brusselator and their stability
-
DOI 10.1016/j.physd.2005.12.005, PII S0167278905005038
-
T. Kolokolnikov, T. Erneux and J. Wei, Mesa-type patterns in the one-dimensional Brusselator and their stability, Physica D, 214 (2006), 63-77. (Pubitemid 43131059)
-
(2006)
Physica D: Nonlinear Phenomena
, vol.214
, Issue.1
, pp. 63-77
-
-
Kolokolnikov, T.1
Erneux, T.2
Wei, J.3
-
20
-
-
12044250363
-
Biological pattern formation: From basic mechanisms to complex structures
-
A. J. Koch and H. Meinhardt, Biological pattern formation: From basic mechanisms to complex structures, Rev. Modern Physics, 66 (1994), 1481-1507. (Pubitemid 24976647)
-
(1994)
Reviews of Modern Physics
, vol.66
, Issue.4
, pp. 1481-1507
-
-
Koch, A.J.1
Meinhardt, H.2
-
21
-
-
33847610410
-
The stability of a stripe for the Gierer- Meinhardt model and the effect of saturation
-
T. Kolokolnikov, M. Ward, W. Sun and J. Wei, The stability of a stripe for the Gierer- Meinhardt model and the effect of saturation, SIAM J. Appl. Dyn. Systems, 5 (2006), 313-363.
-
(2006)
SIAM J. Appl. Dyn. Systems
, vol.5
, pp. 313-363
-
-
Kolokolnikov, T.1
Ward, M.2
Sun, W.3
Wei, J.4
-
22
-
-
12044256206
-
Modeling of turing structures in the chlorite-iodide-malonic acid-starch reaction system
-
I. Lengyel and I. R. Epstein, Modeling of Turing structures in the chlorite-iodide-malonic acid-starch reaction system, Science, 251 (1991), 650-652. (Pubitemid 21916886)
-
(1991)
Science
, vol.251
, Issue.4994
, pp. 650-652
-
-
Lengyel, I.1
Epstein, I.R.2
-
23
-
-
26444473202
-
Turing patterns in the Lengyel-Epstein system for the CIMA reaction
-
DOI 10.1090/S0002-9947-05-04010-9, PII S0002994705040109
-
W. Ni and M. Tang, Turing patterns in the Lengyel-Epstein system for the CIMA reaction, Trans. AMS, 357 (2005), 3953-3969. (Pubitemid 41421390)
-
(2005)
Transactions of the American Mathematical Society
, vol.357
, Issue.10
, pp. 3953-3969
-
-
Ni, W.-M.1
Tang, M.2
-
24
-
-
84972584509
-
Coexistence problem for two competing species models with density-dependent diffusion
-
M. Mimura, Y. Nishiura, A. Tesei and T. Tsujikawa, Coexistence problem for two competing species models with density-dependent diffusion, Hiroshima Math J., 14 (1984), 425-449.
-
(1984)
Hiroshima Math J.
, vol.14
, pp. 425-449
-
-
Mimura, M.1
Nishiura, Y.2
Tesei, A.3
Tsujikawa, T.4
-
25
-
-
34848916953
-
Localized structures in dryland vegetation: Forms and functions
-
E. Meron, H. Yizhaq and E. Gilad, Localized structures in dryland vegetation: Forms and functions, Chaos, 17 (2007), 037109.
-
(2007)
Chaos
, vol.17
, pp. 037109
-
-
Meron, E.1
Yizhaq, H.2
Gilad, E.3
-
26
-
-
63049107118
-
A user's guide to PDE models for chemotaxis
-
MR2448428
-
(MR2448428) T. Hillen and K. J. Painter, A user's guide to PDE models for chemotaxis, J. Math. Biol., 58 (2009), 183-217.
-
(2009)
J. Math. Biol.
, vol.58
, pp. 183-217
-
-
Hillen, T.1
Painter, K.J.2
-
27
-
-
0346801867
-
On the Derivation of a Density Functional Theory for Microphase Separation of Diblock Copolymers
-
DOI 10.1023/A:1025722804873
-
(MR2012976) R. Choksi and X. Ren, On the derivation of a density functional theory for microphase separation of diblock copolymers, J. Stat. Phys., 113 (2003), 151-176. (Pubitemid 38104195)
-
(2003)
Journal of Statistical Physics
, vol.113
, Issue.1-2
, pp. 151-176
-
-
Choksi, R.1
Ren, X.2
-
29
-
-
84866669464
-
-
FlexPDE software. Available from: www.pdesolutions.com.
-
FlexPDE software
-
-
-
30
-
-
84968466504
-
Collocation software for boundary value ode's
-
U. Ascher, R. Christiansen and R. Russell, Collocation software for boundary value ode's, Math. Comp., 33 (1979), 659-579.
-
(1979)
Math. Comp.
, vol.33
, pp. 659-579
-
-
Ascher, U.1
Christiansen, R.2
Russell, R.3
-
31
-
-
0035277877
-
The stability of spike solutions to the one- dimensional Gierer-Meinhardt model
-
MR1818735
-
(MR1818735) D. Iron, M. J. Ward and J. Wei, The stability of spike solutions to the one- dimensional Gierer-Meinhardt model, Physica D, 150 (2001), 25-62.
-
(2001)
Physica D
, Issue.150
, pp. 25-62
-
-
Iron, D.1
Ward, M.J.2
Wei, J.3
-
32
-
-
28444478770
-
Stability of spatially periodic pulse patterns in a class of singularly perturbed reaction-diffusion equations
-
DOI 10.1512/iumj.2005.54.2792
-
(MR2177102) H. van der Ploeg and A. Doelman, Stability of spatially periodic pulse patterns in a class of singularly perturbed reaction-diffusion equations, Indiana Univ. Math. J., 54 (2005), 1219-1301. (Pubitemid 41730645)
-
(2005)
Indiana University Mathematics Journal
, vol.54
, Issue.5
, pp. 1219-1301
-
-
Van Ploeg, H.D.1
Doelman, A.2
-
33
-
-
24144462466
-
Collision versus collapse of droplets in coarsening of dewetting thin films
-
DOI 10.1016/j.physd.2005.06.010, PII S0167278905002605
-
K. B. Glasner and T. P. Witelski, Collision versus collapse of droplets in coarsening of dewetting thin films, Physica D, 209 (2005), 80-104. (Pubitemid 41231001)
-
(2005)
Physica D: Nonlinear Phenomena
, vol.209
, Issue.1-4
, pp. 80-104
-
-
Glasner, K.B.1
Witelski, T.P.2
-
34
-
-
33947231538
-
Coarsening rates for a droplet model: Rigorous upper bounds
-
F. Otto, T. Rump and D. Slepčev, Coarsening rates for a droplet model: Rigorous upper bounds, SIAM J. Math. Analysis, 38 (2007), 503-529.
-
(2007)
SIAM J. Math. Analysis
, vol.38
, pp. 503-529
-
-
Otto, F.1
Rump, T.2
Slepčev, D.3
-
35
-
-
0036435355
-
A renormalization method for modulational stability of quasi-steady patterns in dispersive systems
-
K. Promislow, A renormalization method for modulational stability of quasi-steady patterns in dispersive systems, SIAM J. Math. Anal., 33 (2002), 1455-1482.
-
(2002)
SIAM J. Math. Anal.
, vol.33
, pp. 1455-1482
-
-
Promislow, K.1
-
36
-
-
33947656703
-
Nonlinear asymptotic stability of the semistrong pulse dynamics in a regularized Gierer-Meinhardt model
-
DOI 10.1137/050646883
-
A. Doelman, T. J. Kaper and K. Promislow, Nonlinear asymptotic stability of the semistrong pulse dynamics in a regularized Gierer-Meinhardt model, SIAM J. Math. Anal., 38 (2007), 1760-1787. (Pubitemid 350121916)
-
(2007)
SIAM Journal on Mathematical Analysis
, vol.38
, Issue.6
, pp. 1760-1787
-
-
Doelman, A.1
Kaper, T.J.2
Promislow, K.3
-
37
-
-
0000068099
-
Multi-peak solutions for a wide class of singular perturbation problems
-
J.Wei and M. Winter, Multi-peak solutions for a wide class of singular perturbation problems, J. London Math. Soc., 59 (1999), 585-606.
-
(1999)
J. London Math. Soc.
, vol.59
, pp. 585-606
-
-
Wei, J.1
Winter, M.2
-
38
-
-
41349101280
-
Theory of domain patterns in systems with long-range interactions of Coulomb type
-
066108
-
C. Muratov, Theory of domain patterns in systems with long-range interactions of Coulomb type, Phys. Rev. E., 66 (2002), 066108, 25 pp.
-
(2002)
Phys. Rev. E.
, vol.66
-
-
Muratov, C.1
-
39
-
-
4944224628
-
Bifurcation of spike equilibria in the near-shadow Gierer-Meinhardt model
-
T. Kolokolnikov and M. J. Ward, Bifurcation of spike equilibria in the near-shadow Gierer- Meinhardt model, Discrete and Continuous Dynamical Systems B, 4 (2004), 1033-1064. (Pubitemid 39332902)
-
(2004)
Discrete and Continuous Dynamical Systems - Series B
, vol.4
, Issue.4
, pp. 1033-1064
-
-
Kolokolnikov, T.1
Ward, M.J.2
|