A two-phase Stefan-Signorin problem with the Grbbs-Thomson law is considered m the spherical symmetric care We first prove the existence of a local-in-time classical solution and then rhow the nonexwtenca of a global-in-time classical solutions Finally we study the regularity of the classical solution and show that in general the fint derivate of the solution with respect to the tune vaiable does not continue up to both sides of the interfacs
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