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

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.