A Stefan problem on an evolving surface

作者：Alphonse Amal^*; Elliott Charles M

来源：Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 2015, 373(2050): 20140279.

DOI：10.1098/rsta.2014.0279

• free boundary problems
• Stefan problem
• parabolic equations on moving hypersurfaces
• function spaces for evolving domains

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.

• 出版日期2015-9-13