Skip to Main content Skip to Navigation
Journal articles

A conservation law with spatially localized sublinear damping

Abstract : We consider a general conservation law on the circle, in the presence of a sublinear damping. If the damping acts on the whole circle, then the solution becomes identically zero in finite time, following the same mechanism as the corresponding ordinary differential equation. When the damping acts only locally in space, we show a dichotomy: if the flux function is not zero at the origin, then the transport mechanism causes the extinction of the solution in finite time, as in the first case. On the other hand, if zero is a non-degenerate critical point of the flux function, then the solution becomes extinct in finite time only inside the damping zone, decays algebraically uniformly in space, and we exhibit a boundary layer, shrinking with time, around the damping zone. Numerical illustrations show how similar phenomena may be expected for other equations.
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-01741189
Contributor : Rémi Carles Connect in order to contact the contributor
Submitted on : Friday, March 1, 2019 - 11:15:53 AM
Last modification on : Monday, July 4, 2022 - 9:21:41 AM

Identifiers

Citation

Christophe Besse, Rémi Carles, Sylvain Ervedoza. A conservation law with spatially localized sublinear damping. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2020, 37 (1), pp.13-50. ⟨10.1016/j.anihpc.2019.03.002⟩. ⟨hal-01741189v2⟩

Share

Metrics

Record views

268

Files downloads

146