I. V. Kuznetsov, “Genuinely nonlinear forward-backward ultra-parabolic equations”, Sib. Èlektron. Mat. Izv., 2017, Volume 14,Pages <nobr>710

This article is cited in 3 papers

Differentical equations, dynamical systems and optimal control

Genuinely nonlinear forward-backward ultra-parabolic equations

I. V. Kuznetsov^ab

^a Lavrentyev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, pr. Acad. Lavrentyeva 15, 630090, Novosibirsk, Russia
^b Novosibirsk State University, Pirogova st., 2, 630090, Novosibirsk, Russia

Abstract: In this paper we have proved the existence and uniqueness of entropy solutions to the Dirichlet problem for genuinely nonlinear forward-backward ultra-parabolic equations. We have used a kinetic formulation of entropy solutions which enables also to prove the existence of their traces in the $L^1$ sense.

Keywords: entropy solution, forward-backward ultra-parabolic equation, kinetic formulation.

UDC: 517.95

MSC: 35K70

Received May 3, 2017, published August 1, 2017

Language: English

DOI: 10.17377/semi.2017.14.061