Noncharacteristic mixed problem for nonlinear hyperbolic systems of the first order with zero initial condition (Q1197571)

Investigated are the existence and uniqueness of the solution for problem \[ E(t,x,u)u_ t-\sum_{j=1}^ m A_ j(t,x,u)u_{x_ j}-C(t,x,u)u=F \quad \text{in } [0,T]\times\Omega, \] \[ [I-S(t,x,u)]u=g \quad \text{on }[0,T]\times \partial\Omega, \qquad u|_{t=0}=0 \quad\text{in }\Omega, \] where \(\Omega\subset\mathbb{R}^ m\), \(E,A_ j\;(j=1,\dots,m),C,S\in C^ k(\mathbb{R}^ 1\times\Omega\times \mathbb{R}^ n)\), \(k>(m/2)+(5/2)\) is considered. All functions given here are real.