Abstract
In the present paper we discuss father development of the general scheme of the asymptotic method of differential inequalities and illustrate it applying for some new important cases of initial boundary value problem for the nonlinear singularly perturbed parabolic equations,which are called in applications as reaction-diffusion-advection equations. The theorems which state front motion description and stationary contrast structures formation are proved for parabolic, parabolic-periodic and integro-parabolic problems.
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