Theoretical study demonstrates asymptotic solutions for singularly perturbed Cauchy problems, revealing how rapid oscillations shape system dynamics.
The paper proposes a method for constructing an asymptotic solution to a singularly perturbed Cauchy problem with an exponential rapidly oscillating inhomogeneity. The formalism of the regularization method for the problem is described in detail, the algorithm is substantiated, an asymptotic solution of any order in a small parameter is constructed, and the influence of the rapidly oscillating right-hand side on the asymptotics of the solution is revealed.
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Kalimbetov et al. (2026) studied this question.
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