Geodesic
A singularly perturbed system of first-order partial differential equations
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (1983), pp. 37-41 
T. N. Sysoeva. A singularly perturbed system of first-order partial differential equations. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (1983), pp. 37-41. http://geodesic.mathdoc.fr/item/VMUMM_1983_1_a9/
@article{VMUMM_1983_1_a9,
     author = {T. N. Sysoeva},
     title = {A singularly perturbed system of first-order partial differential equations},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {37--41},
     year = {1983},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1983_1_a9/}
}
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We study the Cauchy problem for the systems as in the title. We find an asymptotic decomposition for the solution and estimate the remainder.