Local weak solvability of a moving boundary problem describing swelling along a halfline
Kota Kumazaki, Adrian Muntean · Networks and Heterogeneous Media · 2019
We obtain the local well-posedness of a moving boundary problem that describes the swelling of a pocket of water within an infinitely thin elongated pore (i.e. on $ [a, +\infty), \ a>0 $). Our result involves fine a priori estimates of the moving boundary evolution, Banach fixed point arguments as well as an application of the general theory of evolution equations governed by subdifferentials.