TY - JOUR

T1 - Quasi-solutions of genuinely nonlinear forward-backward ultra-parabolic equations

AU - Kuznetsov, I. V.

AU - Sazhenkov, S. A.

PY - 2017/10/22

Y1 - 2017/10/22

N2 - In the present paper we have proved the existence of quasi-solutions of genuinely nonlinear forward-backward ultra-parabolic equations. Quasi-solutions are obtained with the help of the vanishing anisotropic temporal diffusion method. Moreover, at the present stage of our research we assume that various choices of temporal artificial diffusion coefficients lead to entropy solutions or to quasi-solutions. The latter assumption is the subject of our further scientific research.

AB - In the present paper we have proved the existence of quasi-solutions of genuinely nonlinear forward-backward ultra-parabolic equations. Quasi-solutions are obtained with the help of the vanishing anisotropic temporal diffusion method. Moreover, at the present stage of our research we assume that various choices of temporal artificial diffusion coefficients lead to entropy solutions or to quasi-solutions. The latter assumption is the subject of our further scientific research.

KW - entropy solution

KW - forward-backward ultra-parabolic equation

KW - genuine nonlinearity condition

KW - kinetic solution

KW - ENTROPY SOLUTIONS

KW - EXISTENCE

KW - SCALAR CONSERVATION-LAWS

KW - STRONG TRACES

KW - KINETIC FORMULATION

UR - http://www.scopus.com/inward/record.url?scp=85033216844&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/894/1/012046

DO - 10.1088/1742-6596/894/1/012046

M3 - Article

AN - SCOPUS:85033216844

VL - 894

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012046

ER -