Abstract:
Systems of first-order semilinear partial differential equations with terms that oscillate at a frequency $\omega\gg1$ in a single variable and are proportional to $\sqrt\omega$ are considered. The Krylov–Bogolyubov–Mitropol'skii averaging method is substantiated for such equations. Based on the two-scale expansion method, an algorithm for constructing complete asymptotics of solutions is proposed and justified.
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