I. V. Kuznetsov, “Kinetic formulation of forward-backward parabolic equations”, Sib. Èlektron. Mat. Izv., 2016, Volume 13,Pages <nobr>930

This article is cited in 5 papers

Differentical equations, dynamical systems and optimal control

Kinetic formulation of forward-backward 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: We have proved that Dirichlet boundary value problem for nonlinear forward-backward parabolic equation has the unique entropy solution. The main difficulty is that initial and final conditions must be formulated in the form of inequalities. We have used here kinetic formulation of the boundary value problem.

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

UDC: 517.95

MSC: 35D30

Received July 21, 2016, published November 21, 2016

Language: English

DOI: 10.17377/semi.2016.13.075