Abstract:
We consider a Cauchy problem for a system of two quasilinear first order partial differential equations with special right-hand sides. We obtain the conditions of a nonlocal solvability of this Cauchy problem. The study of the nonlocal solvability of the Cauchy problem for a system of two quasilinear differential equations with special right-hand sides is based on the method of an additional argument. The proof of the nonlocal resolvability of the Cauchy problem for a system of two quasilinear first order partial differential equations with special right-hand sides relies on global estimates.
Keywords:
first order partial differential equations, Cauchy problem, the method of an additional argument.
Citation:
M. V. Dontsova, “Nonlocal solvability conditions for Cauchy problem for a system of first order partial differential equations with special right-hand sides”, Ufa Math. J., 6:4 (2014), 68–80
\Bibitem{Don14}
\by M.~V.~Dontsova
\paper Nonlocal solvability conditions for Cauchy problem for a~system of first order partial differential equations with special right-hand sides
\jour Ufa Math. J.
\yr 2014
\vol 6
\issue 4
\pages 68--80
\mathnet{http://mi.mathnet.ru/eng/ufa261}
\crossref{https://doi.org/10.13108/2014-6-4-68}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928266790}
Linking options:
https://www.mathnet.ru/eng/ufa261
https://doi.org/10.13108/2014-6-4-68
https://www.mathnet.ru/eng/ufa/v6/i4/p71
This publication is cited in the following 14 articles:
Citation in format AMSBIB
Contact us: