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

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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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     author = {I. V. Zakharova},
     title = {On the asymptotics of the {Goursat} problem with a power boundary layer},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {65--70},
     publisher = {mathdoc},
     volume = {224},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/INTO_2023_224_a7/}
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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/