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A Stefan problem on an evolving surface
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DOI：10.1098/rsta.2014.0279.png)
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Abstract
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We formulate a Stefan problem on an evolving hypersurface and study the well posedness of weak solutions given L-1 data. To do this, we first develop function spaces and results to handle equations on evolving surfaces in order to give a natural treatment of the problem. Then, we consider the existence of solutions for L-infinity data; this is done by regularization of the nonlinearity. The regularized problem is solved by a fixed point theorem and then uniform estimates are obtained in order to pass to the limit. By using a duality method, we show continuous dependence, which allows us to extend the results to L-1 data.
Keywords:
free boundary problems
Stefan problem
parabolic equations on moving hypersurfaces
function spaces for evolving domains
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