×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI