This article is cited in 14 papers

On the formation of sharp transition layers in two-dimensional reaction-diffusion models

V. T. Volkov, N. E. Grachëv, N. N. Nefedov, A. N. Nikolaev

Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: For a singularly perturbed parabolic equation in two dimensions, the formation of a solution with a sharp transition layer from a sufficiently general initial function is considered. An asymptotic analysis is used to estimate the time required for the formation of a contrast structure. Numerical results are presented.

Key words: two-dimensional reaction-diffusion models, asymptotic solution method, formation of contrast structures in solutions, numerical study.

UDC: 519.633.8

Received: 09.01.2007

 English version: Computational Mathematics and Mathematical Physics, 2007, 47:8, 1301–1309

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