Geodesic
On the asymptotics of the Goursat problem with a power boundary layer
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 65-70 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we consider the Goursat problem for a partial differential equation containing a small parameter $\varepsilon$ in the coefficient of the highest derivative. For $\varepsilon=0$, the order of the equation does not decrease, but a singularity appears, which has the nature of a power boundary layer. A solution of the singularly perturbed Gaussian problem is constructed in the form of a formal series in powers of the small parameter. The asymptotic nature of the constructed series is proved.
Keywords: singularly perturbed differential equation, asymptotic integration, power boundary layer
Mots-clés : Goursat problem. 
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I. V. Zakharova. On the asymptotics of the Goursat problem with a power boundary layer. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 65-70. http://geodesic.mathdoc.fr/item/INTO_2023_224_a7/

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