Geodesic
Nonstationary contrast structures in adjacency of the special point
Matematičeskoe modelirovanie, Tome 26 (2014) no. 8, pp. 107-125

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Evolution equations of internal transition layer (ITL) are obtained for reaction-diffusion equation and pseudoparabolic third order equation with the small parameter near high derivatives, which describes different processes in physics, chemistry, biology, particularly, the process of magnetic field generation in the turbulent medium. The case of existence of the point with zero drift velocity (special point) is considered, so that drift velocity doesn't change the sign from the left and from the right of this point. It's shown that drift velocity of the first order of asymptotic expansion for cube balanced nonlinearity, which is widely used in physic applications, equals zero too, second order approximation allows to find drift velocity in the special point. It's shown that ITL runs the special point in limited time.
Keywords: internal transition layer (ITL), contrasting structure (CS), asymptotic method. 
@article{MM_2014_26_8_a7,
     author = {A. A. Bykov and A. S. Sharlo},
     title = {Nonstationary contrast structures in adjacency of the special point},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {107--125},
     publisher = {mathdoc},
     volume = {26},
     number = {8},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2014_26_8_a7/}
}
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A. A. Bykov; A. S. Sharlo. Nonstationary contrast structures in adjacency of the special point. Matematičeskoe modelirovanie, Tome 26 (2014) no. 8, pp. 107-125. http://geodesic.mathdoc.fr/item/MM_2014_26_8_a7/