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 Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 2, Pages 416–437 (Mi izv1816)

A boundary value problem for a quasilinear equation of first order with arbitrary dependence of the direction of the characteristics at the boundary on the unknown function

É. B. Bykhovskii

Abstract: A boundary value problem for the equation
$$\frac d{dx_k}a_k(x,u)+b(x,u)+cu=0$$
is posed and investigated in a domain $\Omega\subset\mathbf R^n$ with boundary $S$. Let $a_\nu$ be the normal component on $S$ of the vector $\vec a=(a_1,…,a_n)$. In contrast to previous papers, an arbitrary dependence of $a_\nu(x,u)$ on $u$ is permitted.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:2, 397–416

Bibliographic databases:

UDC: 517.994
MSC: 35F30

Citation: É. B. Bykhovskii, “A boundary value problem for a quasilinear equation of first order with arbitrary dependence of the direction of the characteristics at the boundary on the unknown function”, Izv. Akad. Nauk SSSR Ser. Mat., 41:2 (1977), 416–437; Math. USSR-Izv., 11:2 (1977), 397–416

Citation in format AMSBIB
\Bibitem{Byk77} \by \'E.~B.~Bykhovskii \paper A~boundary value problem for a~quasilinear equation of first order with arbitrary dependence of the direction of the characteristics at the boundary on the unknown function \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1977 \vol 41 \issue 2 \pages 416--437 \mathnet{http://mi.mathnet.ru/izv1816} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=466916} \zmath{https://zbmath.org/?q=an:0359.35013|0378.35012} \transl \jour Math. USSR-Izv. \yr 1977 \vol 11 \issue 2 \pages 397--416 \crossref{https://doi.org/10.1070/IM1977v011n02ABEH001727}