Stability of $L^\infty$ solutions for hyperbolic systems with coinciding shocks and rarefactions
| dc.creator | Bianchini, Stefano | |
| dc.date | 2000-06-13 | |
| dc.date.accessioned | 2026-07-25T22:48:26Z | |
| dc.description | We consider a hyperbolic system of conservation laws u_t + f(u)_x = 0 and u(0,\cdot) = u_0, where each characteristic field is either linearly degenerate or genuinely nonlinear. Under the assumption of coinciding shock and rarefaction curves and the existence of a set of Riemann coordinates $w$, we prove that there exists a semigroup of solutions $u(t) = \mathcal{S}_t u_0$, defined on initial data $u_0 \in L^\infty$. The semigroup $\mathcal{S}$ is continuous w.r.t. time and the initial data $u_0$ in the $L^1_{\text{loc}}$ topology. Moreover $\mathcal{S}$ is unique and its trajectories are obtained as limits of wave front tracking approximations. | |
| dc.description | 19 pages, 13 figures | |
| dc.identifier | https://arxiv.org/abs/math/0006094 | |
| dc.identifier | http://arxiv.org/abs/math/0006094 | |
| dc.identifier.uri | https://dspace.dare.co.zw/handle/123456789/92695 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35L65 | |
| dc.title | Stability of $L^\infty$ solutions for hyperbolic systems with coinciding shocks and rarefactions | |
| dc.type | text |