ИСТИНА

In this talk we consider a new class of singularly perturbed parabolic periodic boundary value problems for reaction-advection-diffusion equations. We illustrate the principal features of the general scheme of asymptotic method of differential inequalities and apply it to Burgers type equations with modular advection. We construct the interior layer type formal asymptotics and prove the existence of a periodic solution with an interior layer. The accuracy of its asymptotics and asymptotic stability of this solution is also established. We show how the constructed asymptotic can be used to get asymptotic solution of some inverse coefficient problems. In particular, we illustrate our approach by considering the Burgers type equations with modular advection.