A Stefan problem on an evolving surface
2015 ◽
Vol 373
(2050)
◽
pp. 20140279
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Keyword(s):
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 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.
2019 ◽
Vol 24
(10)
◽
pp. 3200-3215
◽
Well-Posedness and Asymptotic Behavior of a Nonclassical Nonautonomous Diffusion Equation with Delay
2015 ◽
Vol 25
(14)
◽
pp. 1540021
◽
2002 ◽
Vol 12
(03)
◽
pp. 431-444
◽
Keyword(s):
1997 ◽
Vol 127
(1)
◽
pp. 181-189
◽
Keyword(s):
2014 ◽
Vol 19
(4)
◽
pp. 524-536
◽