Geodesic
On some systems of partial differential equations with a small parameter in the principal part
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 5th International Conference "Dynamical Systems and Computer Science: Theory and Applications" (DYSC 2023). Irkutsk, September 18-23, 2023, Tome 234 (2024), pp. 50-58

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In this paper, we examine systems of partial differential equations containing a small positive parameter in the principal part. We establish a relationship between solutions of the system with a small parameter and solutions of the limit system obtained if the parameter is equal to zero. We present classes of systems that preserve the properties of regularly perturbed problems under singular perturbations are admit constructing asymptotic solutions by methods of regular perturbation theory.
Keywords: small parameter, singularly perturbed equation, limit problem, Dirichlet problem, Cauchy problem 
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     title = {On some systems of partial differential equations with a small parameter in the principal part},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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I. V. Zakharova; M. V. Falaleev. On some systems of partial differential equations with a small parameter in the principal part. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 5th International Conference "Dynamical Systems and Computer Science: Theory and Applications" (DYSC 2023). Irkutsk, September 18-23, 2023, Tome 234 (2024), pp. 50-58. http://geodesic.mathdoc.fr/item/INTO_2024_234_a6/