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Séminaire Analyse non linéaire et EDP

Horaires : Le mardi 03 janvier 2012, 11h30-12h30

Lieu : IHP, salle 201

A free boundary problem for thin films

Antoine Mellet (Maryland)

The lubrication approximation leads to a fourth order degenerate equation modeling the evolution of small viscous droplets on a solid support (the thin film equation). Along the contact line (the free boundary), the solution must satisfy a gradient condition (contact angle condition). While many existence and regularity results are known for solutions with zero contact angle, the only existence result with non-zero contact angle is due to F. Otto and only holds in some particular framework (Hele-Shaw cell). We consider a singular perturbation approach to generalize Otto's result.

 

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