**J. Gvazava**

## Nonlocal and Initial Problems for Quasilinear,
Nonstrictly Hyperbolic Equations with General Solutions Represented by
Superposition of Arbitrary Functions

**abstract:**

We have selected a class of hyperbolic quasilinear equations of second order,
admitting parabolic degeneracy by the following criterion: they have a general
solution represented by superposition of two arbitrary functions. For equations
of this class we consider the initial Cauchy problem and nonlocal characteristic
problems for which sufficient conditions are established for the solution
solvability and uniquness; the domains of solution definition are described.