Nonlocal Solvability of the Cauchy Problem for a System with Negative Functions of the Variable $t$

Abstract

We obtain sufficient conditions for the existence and uniqueness of a local solution of the Cauchy problem for a quasilinear system with negative functions of the variable $t$ and show that the solution has the same $x$-smoothness as the initial function. We also obtain sufficient conditions for the existence and uniqueness of a nonlocal solution of the Cauchy problem for a quasilinear system with negative functions of the variable $t$.