| Title:
|
The dynamics of weakly interacting fronts in an adsorbate-induced phase transition model (English) |
| Author:
|
Ei, Shin-Ichiro |
| Author:
|
Tsujikawa, Tohru |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
45 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
625-633 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Hildebrand et al. (1999) proposed an adsorbate-induced phase transition model. For this model, Takei et al. (2005) found several stationary and evolutionary patterns by numerical simulations. Due to bistability of the system, there appears a phase separation phenomenon and an interface separating these phases. In this paper, we introduce the equation describing the motion of two interfaces in $\mathbb{R}^2$ and discuss an application. Moreover, we prove the existence of the traveling front solution which approximates the shape of the solution in the neighborhood of the interface. (English) |
| Keyword:
|
reaction-diffusion system |
| Keyword:
|
interaction of fronts |
| Keyword:
|
phase transition model |
| MSC:
|
35B25 |
| MSC:
|
35B40 |
| MSC:
|
35K40 |
| MSC:
|
35K57 |
| MSC:
|
74A50 |
| idZBL:
|
Zbl 1193.35006 |
| idMR:
|
MR2588628 |
| . |
| Date available:
|
2010-06-02T19:00:10Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140058 |
| . |
| Reference:
|
[1] S.-I. Ei: The motion of weakly interacting pulses in reaction-diffusion systems.J. Dynam. Differential Equations 14 (2002), 85–137. Zbl 1007.35039, MR 1878646 |
| Reference:
|
[2] S.-I. Ei and T. Ohta: Equation of motion for interacting pulse.Phys. Rev. E 50 (1994), 4672–4678. |
| Reference:
|
[3] M. Eiswirth, M. Bär, and H. H. Rotermund: Spatiotemporal selforganization on isothermal catalysts.Physica D 84 (1995), 40–57. |
| Reference:
|
[4] M. Funaki, M. Mimura, and T. Tsujikawa: Travelling front solutions arising in the chemotaxis-growth model.Interfaces and Free Boundaries 8 (2006), 223–245. MR 2256842 |
| Reference:
|
[5] M. Hildebrand: Selbstorganisierte nanostrukturen in katakyschen oberflächenreaktionen.Ph.D. Dissertation, Mathematisch–Naturwissenschaftlichen Fakultät I, Humboldt–Universität, Berlin 1999. |
| Reference:
|
[6] M. Hildebrand, M. Ipsen, H. S. Mikhailov, and G. Ertl: Localized nonequailibrium nanostructures in surface chemical reactions.New J. Phys. 5 (2003), 61.1–61.28. |
| Reference:
|
[7] M. Hildebrand, M. Kuperman, H. Wio, and A. S. Mikhailov: Self-organized chemical nanoscale microreactors.Phys. Rev. Lett. 83 (1999), 1475–1478. |
| Reference:
|
[8] K. Kuto and T. Tsujikawa: Pattern formation for adsorbate-induced phase transition model.RIMS Kokyuroku Bessatsu B3 (2007), 43–58. MR 2408125 |
| Reference:
|
[9] A. v. Oertzen, H. H. Rotermund, A. S. Mikhailov, and G. Ertl: Standing wave patterns in the CO oxidation reaction on a Pt(110) surface: experiments and modeling.J. Phys. Chem. B 104 (2000), 3155–3178. |
| Reference:
|
[10] Y. Takei, T. Tsujikawa, and A. Yagi: Numerical computations and pattern formation for adsorbate-induced phase transition model.Sci. Math. Japon. 61 (2005), 525–534. MR 2140113 |
| Reference:
|
[11] Y. Takei, M. Efendiev, T. Tsujikawa, and A. Yagi: Exponential attractor for an adsorbate-induced phase transition model in non smooth domains.Osaka J. Math. 43 (2006), 215–237. MR 2222411 |
| Reference:
|
[12] T. Tsujikawa: Singular limit analysis of an adsorbate-induced phase transition model.Preprint. |
| Reference:
|
[13] T. Tsujikawa and A. Yagi: Exponential attractor for an adsorbate-induced phase transition model.Kyushu J. Math. 56 (2002), 313–336. MR 1934129 |
| . |
