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.
