A conservation law with spatially localized sublinear damping (Christophe Besse, Toulouse)

06.03.2018 14:00

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 and decays algebraically uniformly in space. We will present some numerical illustrations which will show how similar phenomena may be expected for other equations.

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salle 623, Séminaire d'analyse numérique

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