On the Convergence Rate of Vanishing Viscosity Approximations
| dc.creator | Bressan, Alberto | |
| dc.creator | Yang, Tong | |
| dc.date | 2003-07-10 | |
| dc.date.accessioned | 2026-07-07T04:59:34Z | |
| dc.date.available | 2026-07-07T04:59:34Z | |
| dc.description | Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound $\big\|u(t,\cdot)-u^\ve(t,\cdot)\big\|_{Ł^1}= Ø(1)(1+t)\cdot \sqrt\ve|\ln\ve|$ on the distance between an exact BV solution $u$ and a viscous approximation $u^\ve$, letting the viscosity coefficient $\ve\to 0$. In the proof, starting from $u$ we construct an approximation of the viscous solution $u^\ve$ by taking a mollification $u*ϕ_{\strut \sqrt\ve}$ and inserting viscous shock profiles at the locations of finitely many large shocks, for each fixed $\ve$. Error estimates are then obtained by introducing new Lyapunov functionals which control shock interactions, interactions between waves of different families and by using sharp decay estimates for positive nonlinear waves. | |
| dc.description | 34 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/math/0307141 | |
| dc.identifier | http://arxiv.org/abs/math/0307141 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68039 | |
| dc.subject | Analysis of PDEs | |
| dc.title | On the Convergence Rate of Vanishing Viscosity Approximations | |
| dc.type | text |