Geodesic
Numerical simulation of unstable processes in phase decomposition problem
Matematičeskoe modelirovanie, Tome 14 (2002) no. 2, pp. 27-38

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We carry out numerical simulation of phase decomposition processes in binary alloys for a conservative phase field system. For the case $x\in\mathbb R^1$ explicit and implicit difference schemes are proposed. Numerical results illustrate the main stages of the process dynamics: the interface motion, the evolution and bifurcation of a “soliton”, and the motion and bifurcation of an oscillating singularity. 
@article{MM_2002_14_2_a2,
     author = {D. A. Kulagin and G. A. Omel'yanov and N. O. Ordinartseva},
     title = {Numerical simulation of unstable processes in phase decomposition problem},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {27--38},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2002_14_2_a2/}
}
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D. A. Kulagin; G. A. Omel'yanov; N. O. Ordinartseva. Numerical simulation of unstable processes in phase decomposition problem. Matematičeskoe modelirovanie, Tome 14 (2002) no. 2, pp. 27-38. http://geodesic.mathdoc.fr/item/MM_2002_14_2_a2/