Abstract:
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In this paper, we study the spatial behavior of three phase-field models. First, we consider the Cahn-Hilliard equation and
we obtain the exponential decay of solutions under suitable assumptions on the data. Then, for the classical isothermal
phase-field equation (i.e., the Allen-Cahn equation), we prove the nonexistence and the fast decay of solutions and, for
the nonisothermal case governed by the Fourier law, we obtain a Phragm ́
en-Lindel ̈
of alternative of exponential type,
respectively. |