The energy method can be used to identify well-posed initial boundary value problems for quasilinear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete system can be used to construct stable finite difference equations for these problems at the linear level. In this paper we apply these techniques to some test ...

A classical solution of the problem for a quasilinear hyperbolic equation in case two independent variables with given conditions desired function on characteristic lines is obtained. The reduced to system equations completely continuous operator. We constructed unique by method successive approximations and showed necessary sufficient smoothness matching functions.

We describe the point and contact equivalence groupoids of an important class two-dimensional quasilinear hyperbolic equations. In particular, we prove that this is normalized in usual sense with respect to transformations, its groupoid generated by first-order prolongation groupoid, vertex group wave equation a family admissible transformations between trivially Darboux-integrable

The Cauchy problem for a quasilinear system of hyperbolic-parabolic equations is addressed with the method linearization and fixed point. Coupling between hyperbolic parabolic variables allowed in we do not assume Friedrich's symmetrizability system. This coupling results linear energy estimates that prevent application Banach's contraction principle. A metric point theorem developed order to c...