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Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2020, Volume 55, Pages 60–78
DOI: https://doi.org/10.35634/2226-3594-2020-55-05
(Mi iimi391)
 

MATHEMATICS

Sufficient conditions of a nonlocal solvability for a system of two quasilinear equations of the first order with constant terms

M. V. Dontsova

National Research Lobachevsky State University of Nizhny Novgorod, pr. Gagarina, 23, Nizhny Novgorod, 603950, Russia
References:
Abstract: We consider a Cauchy problem for a system of two quasilinear equations of the first order with constant terms. The study of the solvability of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms in the original coordinates is based on the method of an additional argument. Theorems on the local and nonlocal existence and uniqueness of solutions to the Cauchy problem are formulated and proved. We prove the existence and uniqueness of the local solution of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms, which has the same smoothness with respect to $x$ as the initial functions of the Cauchy problem. Sufficient conditions for the existence and uniqueness of a nonlocal solution of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms are found; this solution is continued by a finite number of steps from the local solution. The proof of the nonlocal solvability of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms relies on global estimates.
Keywords: a system of quasilinear equations, the method of an additional argument, Cauchy problem, global estimates.
Received: 04.11.2019
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: M. V. Dontsova, “Sufficient conditions of a nonlocal solvability for a system of two quasilinear equations of the first order with constant terms”, Izv. IMI UdGU, 55 (2020), 60–78
Citation in format AMSBIB
\Bibitem{Don20}
\by M.~V.~Dontsova
\paper Sufficient conditions of a nonlocal solvability for a system of two quasilinear equations of the first order with constant terms
\jour Izv. IMI UdGU
\yr 2020
\vol 55
\pages 60--78
\mathnet{http://mi.mathnet.ru/iimi391}
\crossref{https://doi.org/10.35634/2226-3594-2020-55-05}
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