Abstract:
Using compactness methods for functions from the scale of Banach spaces, we prove the solvability of the problem with nonlinear latent heat of matter fusion in Stefan’s condition. An initial boundary value problem in a non-cylindrical domain with a given curved boundary of class W 1 is preliminarily investigated, for which we obtain uniform estimates necessary for the main problem. Then we consider a problem in which the coefficient of the latent specific heat of fusion in the condition on the unknown boundary is a function of the size of the thawing zone s(t). This technique can also be applied to more general equations. The studied problem describes the processes of transition of matter from one state to another. As a result, the regular global in time solvability of the one-phase Stefan problem for the nonlinear parabolic equation is established. The initial data belong only to the class W 1, while the phase transition boundary defined together with the solution belongs to W 1.
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