Solutions of a problem of ‘reaction–diffusion’ type with internal transition layers in the case of non-linearity of quadratic type

I. V. Nedelko

M. V. Lomonosov Moscow State University

Abstract: We find conditions under which solutions with internal transition layers are formed in a singularly perturbed parabolic problem of ‘reaction–diffusion’ type and prove the existence of similar stationary solutions.

Keywords: contrast structures, internal transition layer.

UDC: 517.956

MSC: 35B20, 35B25, 35B30, 35B40, 35B45, 35C20, 35D05, 35J25, 35J60, 35K57, 35K55, 35K60, 35R45

Received: 17.05.2007

DOI: 10.4213/im2666

 English version: Izvestiya: Mathematics, 2009, 73:1, 151–170

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