Center stable manifolds for quasilinear parabolic pde and conditional stability of nonclassical viscous shock waves
| dc.creator | Zumbrun, Kevin | |
| dc.date | 2008-11-17 | |
| dc.date | 2009-01-13 | |
| dc.date.accessioned | 2026-07-07T12:28:15Z | |
| dc.date.available | 2026-07-07T12:28:15Z | |
| dc.description | Motivated by the study of conditional stability of traveling waves, we give an elementary $H^2$ center stable manifold construction for quasilinear parabolic PDE, sidestepping apparently delicate regularity issues by the combination of a carefully chosen implicit fixed-point scheme and "damping-type" $H^s$ energy estimates of a type familiar from the study of hyperbolic--parabolic and relaxation systems. An important feature of these methods is that they generalize to situations such as the hyperbolic--parabolic or relaxation case for which parabolic-type smoothing estimates are unavailable. As an application, we show conditional stability of Lax- or undercompressive shock waves of general quasilinear parabolic systems of conservation laws by a pointwise stability analysis on the center stable manifold. | |
| dc.identifier | https://arxiv.org/abs/0811.2788 | |
| dc.identifier | http://arxiv.org/abs/0811.2788 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215475 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Center stable manifolds for quasilinear parabolic pde and conditional stability of nonclassical viscous shock waves | |
| dc.type | text |