## Initial-boundary value problems for nonlinear systems of conservation laws.(English)Zbl 0868.35069

Summary: The system of conservation laws $u_t+ [f(u)]_x=0$ is considered on a domain $$\{(t,x); t\geq 0, x>\Psi(t)\}$$, for a continuous map $$\Psi:[0,\infty)\to \mathbb{R}$$, subject to the initial condition $$u(0,x)=\overline u(x)$$, $$x>\Psi(0)$$. We prove two global existence theorems for two distinct types of boundary conditions, with data of small total variation.

### MSC:

 35L65 Hyperbolic conservation laws 35L50 Initial-boundary value problems for first-order hyperbolic systems

### Keywords:

global existence; data of small total variation
Full Text: