I. V. Kuznetsov, S. A. Sazhenkov, “Anisotropic vanishing diffusion method applied to genuinely nonlinear forward-backward ultra-parabolic equations”, Sib. Èlektron. Mat. Izv., 2018, Volume 15,Pages <nobr>1158

This article is cited in 1 paper

Differentical equations, dynamical systems and optimal control

Anisotropic vanishing diffusion method applied to genuinely nonlinear forward-backward ultra-parabolic equations

I. V. Kuznetsov^ab, S. A. Sazhenkov^ba

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

Abstract: The results formulated in (I.V. Kuznetsov, Sib. Elect. Math. Rep. 14 (2017), 710–731) are extended onto the multi-time case. We prove existence and uniqueness of kinetic solutions to genuinely nonlinear forward-backward ultra-parabolic equations and show that kinetic solutions do not depend on the anisotropic elliptic regularization.

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

UDC: 517.95

MSC: 35K92

Received June 26, 2018, published October 15, 2018

Language: English

DOI: 10.17377/semi.2018.15.094