A nonlinear singularly perturbed system of parabolic equations in a two-dimensional domain is considered. The system can be used to simulate the motion of an autowave front in a model of the evolution of urban ecosystems in the case of an inhomogeneous medium whose parameters vary with time. An asymptotic analysis of the problem is performed using methods of the theory of contrast structures. An asymptotic approximation of a front-type solution of the zero and first orders is obtained.
87.10.Ed Ordinary differential equations
$^1$Department of Mathematics, Faculty of physics, Lomonosov Moscow State University, chair of Mathematics.\
$^2$Department of Mathematics, Faculty of physics, Lomonosov Moscow State University
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