Existence and Stability of Periodic Contrast Structuresin the Reaction–Advection–Diffusion Problem in the Case of a Balanced Nonlinearityстатья
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Аннотация:We study a singularly perturbed periodic problem for the parabolic reaction–
advection–diffusion equation with small advection. We consider the case in which there exists
an internal transition layer under the conditions of balanced nonlinearity. An asymptotic expansion
of the solution is constructed. To substantiate this asymptotics, we use the asymptotic
method of differential inequalities. The Lyapunov asymptotic stability of the periodic solution
is analyzed.