Unstable Free Boundary Problems in Solid Combustion

  • Georg Weiss (University of Tokyo)
A3 01 (Sophus-Lie room)


We discuss unstable free boundary problems arising in SHS/gasless combustion and smoldering combustion. We focus on a result obtained in collaboration with Régis Monneau (CERMICS, Paris) concerning the stationary equation \[ \Delta u = -\chi_{\{ u>0\}}\] arising as first order approximation in solid combustion: some partial regularity holds for maximal solutions of this equation. In particular, in two space dimensions the interface consists locally of a finite number of $C1$-arcs meeting in quadruple junctions.

Anne Dornfeld

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