Geodesic
Solution of the singularly perturbed Cauchy problem with a ``weak'' turning point of the limit operator
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 55-64.

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In this paper, we propose a method for constructing an asymptotic solution to a singularly perturbed Cauchy problem in the case of violation of the stability conditions for the spectrum of the limit operator. In particular, we consider a problem with a turning point where eigenvalues coincide at $t=0$.
Keywords: singularly perturbed problem, turning point, regularization method. 
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A. G. Eliseev; P. V. Kirichenko. Solution of the singularly perturbed Cauchy problem with a ``weak'' turning point of the limit operator. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 55-64. http://geodesic.mathdoc.fr/item/INTO_2021_192_a5/

[3] Bobodzhanov A. A., Safonov V. F., “Regulyarizovannaya asimptotika reshenii integro-differentsialnykh uravnenii s chastnymi proizvodnymi s bystro izmenyayuschimisya yadrami”, Ufim. mat. zh., 10:2 (2018)

[4] Voevodin V. V., Vychislitelnye osnovy lineinoi algebry, Nauka, M., 1977

[5] Eliseev A. G., Lomov S. A., “Teoriya singulyarnykh vozmuschenii v sluchae spektralnykh osobennostei predelnogo operatora”, Mat. sb., 131 (173):4 (12) (1986), 544–-557

[6] Eliseev A. G., Salnikova T. A., “Postroenie resheniya zadachi Koshi v sluchae «slaboi» tochki povorota predelnogo operatora”, Tr. konf. «Matematicheskie metody i prilozheniya» (27-31 yanvarya 2011 g. RGSU), 2011, 46–52

[7] Kucherenko V. V., “Asimptotika resheniya sistemy $A(x,-ih{\partial}/{\partial x})$ pri $h\rightarrow 0$ v sluchae kharakteristik peremennoi kratnosti”, Izv. AN SSSR. Ser. mat., 38:3 (1974), 625–-662

[8] Lomov S. A., Vvedenie v obschuyu teoriyu singulyarnykh vozmuschenii, Nauka, M., 1981