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Carnegie Mellon NSF logoCenter for Nonlinear Analysis
Ruediger Landes
Afilliation: University of Oklahoma

Title: Supersolutions in the theory of wavefronts.

Abstract: Here we consider wave front like phase transitions of solutions of a nonlinear boundary value problem for the heat eqaution. The nonlinearity is typical Allen–Cahn function but acting on (parts of) the boundary and not in the interior of the domain. That parabolic problem is used to model phase transitions in the theory of boiling liquids. Employing weak supersolutions we provide bounds for the propagation speed of such an phase transition. Also we construct stable supersolutions to initial configurations which have locally supercritical values.