4 research outputs found
Mean curvature flow with triple junctions in higher space dimensions
We consider mean curvature flow of n-dimensional surface clusters. At
(n-1)-dimensional triple junctions an angle condition is required which in the
symmetric case reduces to the well-known 120 degree angle condition. Using a
novel parametrization of evolving surface clusters and a new existence and
regularity approach for parabolic equations on surface clusters we show local
well-posedness by a contraction argument in parabolic Hoelder spaces.Comment: 31 pages, 2 figure
Smooth solutions to a class of free boundary parabolic problems
We establish existence, uniqueness, and regularity results for solutions to a class of free boundary parabolic problems, including the free boundary heat equation which arises in the so-called "focusing problem" in the mathematical theory of combustion. Such solutions are proved to be smooth with respect to time for positive
t
t
, if the data are smooth
Multiplicity and stability of travelling wave solutions in a free boundary combustion-radiation problem
We study travelling wave solutions of a one-dimensional two-phase Free Boundary Problem, which models premixed flames propagating in a gaseous mixture with dust. The model combines diffusion of mass and temperature with reaction at the flame front, the reaction rate being temperature dependent. The radiative effects due to the presence of dust account for the divergence of the radiative flux entering the equation for temperature. This flux is modelled by the Eddington equation. In an appropriate limit the divergence of the flux takes the form of a nonlinear heat loss term. The resulting reduced model is able to capture a hysteresis effect that appears if the amount of fuel in front of the flame, or equivalently, the adiabatic temperature is taken as a control parameter